Product Description
Clear, lively style covers all basics of theory and application, including Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Diagraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics.
... Read more

Customer Reviews (9)

Finally, a mathematical gem!
This book is great. I am a law student with dated mathematical background, and needed a primer on graph theory to work for a project. This book is just great, explaining every concept carefully, and even providing a tiny bibliography at the end of each chapter.
Just remember to go through the appendix on sets, functions, theorems and proofs (principle of induction).

Topics in Graph Theory
This book is great for a course in topics in graph theory. It gives some theory followed by applications. It requires some mathematical maturity since some of the exercises require proofs. I would recommend this book for junior and senior undergraduates, and perhaps some graduate students who need graph theory.

The Holy Grail of Graph Theory
This is, for all purposes, the Holy Grail of Graph Theory.It is older, but still very much applicable.As a computer scientist (instructor and Masters degree student), I highly recommend this for students studying Discrete Mathematics and Graph Theory.

It has several examples throughout and the presentation is excellent.Many books on mathematics from this 'era' tend to be overly wordy and full of poorly explained examples and topics.This book suffers very little from this problem.

I recommend this to anyone looking for a good introductory book on Graph Theory.It also makes an excellent reference book for even the experienced individual.

Chemistry, Neural Nets, Matrix Manipulation -- all here
While working on my math degree I wanted some light reading on Graph Theory for completing some side projects.This book hit the spot, and the examples saved me.

Chartrand uses applications from every field of interest (e.g. finance, Chemistry, Physics, games, social psychology, computers, etc.)Who would have thought that while reading a math book that a friendly discussion of social psychology would pop-up?Well, that's how Chartrand is able to keep us moving through the pages; he uses the common to reveal the mysteries of Graph Theory. Who doesn't know about the Tower of Hanoi or the Knight's Tour or the one-boat-fox-and-chickens problems? All of these classics make for ready connecting points, leading us into profound restatements of well-known problems.Not much space is devoted to creating artificial problems for which we must be convinced need solving, and so the book is rather thin (a real bonus for those of us who don't want to spend a month in a math book).

Picking up the book after having read it so long ago, I was happy to find that the chapters are nearly autonomous and can be profitably read by themselves -- so keep it as a reference and jump in as the need arises, you'll be both entertained and mathematically illumined.

My only complaint is that the writing style is rather thick with mathematical lingo (seemingly) for the sake of being technically pithy.I am not convinced that such is necessary for a good math book.

Excellent overview for those with solid math background
This book is excellent, especially if you already have a pretty good background in math.I don't... high school math through calculus, almost all of which I've forgotten.But the appendix gets you up to speed on the basics of sets, functions, and proofs using mathematical induction.That was enough for me to get a lot out of all but the last chapter, which deals with matrices and groups.Although I have to admit that I occasionally needed to read an example four or five times before I really got it.

I definitely recommend this book for anyone interested in graph theory and to any serious software developer (which I why I picked it up).The ideas presented are directly applicable to that line of work. ... Read more

Product Description
This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory.It should be accessible to motivated upper-level undergraduates. ... Read more

Customer Reviews (2)

Very Interesting; Just the Right Pace
I have found this book very helpful in trying to understand both the basics of graph theory and advanced topics like spectral graph theory. This book does not use brooding overly complex language and moves through the material at a very good pace. It gives an exciting taste of some beautiful examples in graph theory, such as the Coxeter graph, to motivate research in it, and moves at just the right pace. It doesn't take forever to explain simple concepts and lets the reader quickly understand many concepts, even somewhat advanced ones, without making the material too difficult.

The reader is very much given a choice as to how much detail s/he wants to absorb. One can have a brief glance at just the theorems and definitions, which are easy to find using the index, and are well-stated. Or, one can briefly glance at the text without going into too much detail but still get the big picture. Finally, even complete understanding can be achieved without taking up too much time.

I highly recommend this book for a first or second course in graph theory, to anyone looking to start research in graph theory, for teachers who wish to motivate their students to start research in graph theory, as a reference, or as a quick borrow to learn a concept or two, making this book very important for any library.

an introduction to an interesting subject
--The first part of the book is devoted to quite hard chapters on transitive, arc-transitive graph,homomorphism, etc.

--The second part is about Matrix theory, interlacing, strongly regular graph, two graph, generalized line graph, etc it is the main part of the book.

--The third part is about cut, flows, Knots, etc.

This book can serve as a nice introduction to thesubject of Graph theory.

Nevertheless:

--This book lacks some more example, for this see "distance regular graph".

--It is sketchy on chromatic polynomial, planar graph.

--The original book by Norman Biggs is shorter, smarter, nicer ... Read more

Product Description
Student's love Schaum's--and this new guide will show you why! Graph Theory takes you straight to the heart of graphs. As you study along at your own pace, this study guide shows you step by step how to solve the kind of problems you're going to find on your exams. It gives you hundreds of completely worked problems with full solutions. Hundreds of additional problems let you test your skills, then check the ansers. So if you want to get a firm handle on graph theory--whether to ace your graph course, to supplement a course that uses graphs, or to build a solid basis for future study--there's no better tool than Schaum's. This guide makes a wonderful supplement to your class text, but it is so comprehensive that it can even be used alone as a complete graph theory independent study course! ... Read more

Customer Reviews (6)

A Wonderful Introduction to Graph Theory
I think the Schaum's Outline, Graph Theory, by V.K. Balakrishanan is a wonderful introduction to graph theory. I decided to write this review after reading some negative reviews of this book.I'm trained in mathematics so I understand that theorems and proofs must be studied carefully and thoughtfully before they make sense. But if one takes the necessary time with this book he or she will come away with a good grasp of the fundamentals of graph theory.Such major topics as connectivity, Hamiltonian graphs, trees, network flows, matching and factors, graph embeddings, and graph coloring are thoroughly covered with carefully worked out problems and proofs. In the chapter on Hamiltonian graphs, for example, we learn about the sequence of theorems by Dirac, Ore, Posa, Bondy, and Chvatal - each one implying its predecessor. The Kruskal and Prim algorithms are covered in the chapter on trees and there is even a mention of matroids here. The max-flow-min-cut theorem by Ford and Fulkerson is derived in the chapter on network flows and from this Menger's theorem is deduced. Tutte's famous theorem on matchings in general graphs is covered in the chapter on matching and factors.The beautiful proof alone by Lovasz of Tutte's theorem is worth the price of the book. Important theorems by Whitney, Konig, Hall, and Dilworth are all here. The chapter on graph coloring has the theorems of Brooks, Vizing, and Heawood, and even a section on reducible graphs and unavoidable sets (which provides the basis for the proof of the Four Color Theorem)What's missing?This book was published in 1997 so there is no mention of the Graph Minor Theorem. But if a student were to master the material in the Schaum's Outline, Graph Theory, he or she would be ready to tackle the Graph Minor Theorem.

Wonderful Reference For Graph Theory
This book is wonderful in my eyes. However, I do not recommend most Schaum's Outlines as textbooks, but as supplements to texts. They just contain too much. This book is good reference to have if you're doing a course in graph theory or if your work involves graph theory. I highly recommend it for reference use.

Not up to the standard of most Schaum's outlines
I have bought and used many Schaum's outlines on various subjects in math and science, and I would say that this outline on graph theory is one of the worst. Most Schaum's outlines give you the theory in small doses, with plenty of diagrams to explain the concepts. This outline reads more like one of the textbooks on the subject, however. Theorems and their illustrations are poorly presented, and the author could not have made the subject matter drier and more unappealing if he had tried. You might be able to get something out of it if you are a student of pure mathematics, but you will definitely be disappointed in this book if you are a computer science student. If you are already using a bad textbook for a class in graph theory, this book will only add to your collection of bad unreadable texts on the subject. For computer science students, I suggest that you check out the chapters on graph algorithms in Introduction to Algorithms by Cormen et al. That book has pseudocode, explanations, and diagrams to help you work out implementations of various graphing algorithms.

This book is $$$ for a reason
This book was an absolute hell to contend with.I've taken two courses in Graph Theory, using Robin J. Wilson's Introduction to Graph Theory and this cheap broadsheet, respectively.Wilson's book is the one to use!It's extremely well-written, even fun to read--the reviews on Amazon will bear that out.

In the second graph theory course that I took (to refresh and refine my understanding), the professor chose the Schaum text solely for its low cost--he thought he was doing the students a service.Hardly.

No thought whatsoever has been put into the readability of this book.The tiny dark-grey font on light-grey paper is a simple enough design flub that makes reading past even two or three pages at a time almost unbearable.Defining terms is seen as a chore to be compacted--a single page at the beginning of each chapter might try to define 10-15 terms, just to get them out of the way.It becomes a mess of bold print that the reader is forced to continually return to because the definitions come with no context nor examples by which to remember them.In the end, the reader realizes that 2/3 of the book is just list after list of badly-worded questions following under-scripted lessons.

Look, it's not even worth writing any more about, the text frustrates me so much.There's only two other reviews on this page, and I'd place money on them being written by the author himself.Save yourself the $$$ and the hassle, and just go buy Wilson's book.Trust me.

Good Book. I recommend it.
In general, the book not requires study in advance, but it is better for reference. I'm a software engineer and the book's treatment of "Shortest Path" and "Connectivity" problems is very usefull. Good for fast remember of the subject. ... Read more

Product Description

The third edition of this standard textbook of modern graph theory has been carefully revised, updated, and substantially extended. Covering all its major recent developments, Graph Theory can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field.

Customer Reviews (4)

For the mathematically mature
This is an excellent book, but if you are looking for an introductory book with examples you should look elsewhere, like the book by Gary Chartrand:
Introductory Graph Theory.
The definitions are very concise and not always visual, so you might have to take a pencil and paper as you go through this book and try to
draw a picture corresponding to what has been written.
Still, there is a lot of material here, thanks to the concision, and for a graduate student it's hard to think of a better introduction.

Electronic Edition
If you want a look at the contents, the author also offers a full, free electronic edition of this book from his website. Seach for "Graph Theory Diestel" and his pages will come up. You are not able to print the free electronic edition, but you can save it for offline reading.

I love this book. I purchased the print version after reading the electronic edition.

Great book
I bought this book because my Graph Theory teacher recommended us to read it. It is very complete and it explains very well the subject.

Somewhat technical but well written
Not a book that you can really judge well on one reading:
study is necessary.
The authorpresents the diagrams and proofs well.
He covers the main topics in graph theory:
"Matching,"
"Connectivity,"
"Planar Graphs,"
"Coloring,"
"Flows
"Ramsey Theory for Graphs,"
"Hamilton Cycles,"
"Random Graphs,"
"Minors, Trees and Well-Quasi-Ordering."
and Infinite graphs.
It is a text for graduate school topology in which the theory of graphs
is covered in detail.
I could wish for more on Ramsey theory,
but the author's are the only graph diagrams in that area that I've found. ... Read more

Product Description
A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler’s formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. Exercises are included at the end of each chapter. "The topics are so well motivated, the exposition so lucid and delightful, that the book’s appeal should be virtually universal ... Every library should have several copies" — Choice 1976 edition.
... Read more

Customer Reviews (8)

Elementary yet comprehensive enough
This book introduces graph theory terminology and elementary results to the absolute beginner. It does a nice job of presenting the material in the format "motivation-example-definitions-theorem-proof-remarks", which I find pedagogical.

Interspersed throughout the text are some historical remarks and a lot of author's personal opinions on what mathematics is or should be. This last piece of the text I liked least, since I do not agree with the author many times. He defends the position that "pure mathematics" is "real mathematics", and that "applied mathematics" follows from the "real thing" (he actually states this literally in the introduction of the book). This view has been debunked so many times along the history of the subject that it is quite irritating to see it expressed so categorically.

But the book is not about math philosophy, so I recommend it as a warm up to those interested in more heavy-duty graph theory.

Very Good Introduction
This book provides a good but not rigorousgreat introduction to graph theory. The best audience is someone with mathematical ability but little education beyond high school or introductory math. That is, knowledge of analysis or higher is not required. Having finished this book, one could go on to the book entitled graph theory by the same publisher. It's hard to beat Dover's prices and selection for math books. The style of the book is conversational except for one more proof-oriented chapter. At the end of each chapter are graded problems with answers, a great plus for self-study.

Wonderful
Wonderful book to read!If you want to get started in graph theory, this is your first stop.Go through all the proofs and problems, and you're on your way!

Fun intro to graph theory
I like this book as an intro to graph theory.I already had a little background in graph theory and a graduate degree in mathematics before I got this book, but I think that less experienced readers with an interest in pure math will enjoy this book.It's readable and conversational, and special attention is given to introducing pure mathematics and proof.

Nice Introduction
One of the better Dover books I've picked up... but keep in mind it is a (very basic) introduction.

The book gives an introduction to graph theory (take the "introduction to" part of the title very seriously).To give an idea of the depth of this book, I read this book in about 6 hours prior to taking a course in graph theory (an undergraduate and graduate student mixed course), and the material in the book was covered in class in about 4 lectures (there were about 30 lectures in the course).This isn't to say the book isn't good (because it is), but I just have to emphasize it is a basic introduction.

What gives this book 5 stars is that it was written very well and made the material very interesting.I would recommend this book to someone looking to understand the very basics of graph theory, but I would not to someone looking for a thorough introduction to graph theory.

For reference, titles of chapters: 1) Pure Mathematics; 2) Graphs; 3) Planar Graphs; 4) Euler's Formula; 5) Platonic Graphs; 6) Coloring; 7) The Genus of a Graph; 8) Euler Walks and Hamilton Walks. ... Read more

Product Description
These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline. ... Read more

Customer Reviews (10)

Look it over carefully
I would exercise some caution before purchasing or adopting this text.While many reviewers find the style exuberant and humorous, I find it a bit breezy and even flip, at the expense of clarity.Here's an example, the definition of an SDR:

Given some family of sets X, a system of distinct representatives, or SDR, for
the sets in X can be thought of as a "representative" collection of distinct
elements from the sets of X.For instance, ....[What follows is a collection
of 5 sets and an SDR for them, along with a subcollection of 4 sets that doesn't
have an SDR.]

"Can be thought of"?Such tentative language is not helpful, and I'm not sure that the example would nail it down for the uninitiated.

The third chapter of the book (there are just three), "Infinite combinatorics and graphs", is what initially caught my attention, but the primary emphasis here is symbolic logic and abstract set theory.Very interesting topics, but the connection to combinatorics is a bit thin.

succinct and eloquent
I find the book to explain exactly what it intends to, providing pertinent examples where useful. I wish there were more examples, actually, but there is something to be said for being concise. The problems are well-organized and good problems. Also, it is a nice, sturdy hardcover version with non-glossy pages, which makes it easy to carry around without getting it beat up and easy on the eyes under fluorescent lights.

A highlight of my undergraduate math education
This is by far the best math book I have ever read. The authors present the material in a clear but also incredibly engaging way. The problems are interesting and spot-on in terms of difficulty for the sophomore to junior level introductory course. Those looking for a more classical definition-theorem-proof style textbook should look elsewhere. This is not to say that the textbook lacks rigor (the proofs are very precise), but that it reads more like a narrative, so that it might not serve as the best reference. For the student, however, there really isn't much more you could ask for in a math book.

Not bad, but not the best
The book does an ok job of explaining things.However, there are very few examples.

Doesn't Give Away the Store...
My background:I am an MIS major that discovered too late that he had an intense love for the mathematics behind the magic of computer science.I had previously only taken business calc(!) and Discrete Math (for CS majors).The book assigned was Tucker's book which does a great job on generating functions, but loses brevity completely when entering the field of recursive relations.

This book's explanations dealing with poker hands did what Tucker's and Grimaldi's books left me hanging on.Treatment on the binomial theorem and its related applications was also very thorough and at an acceptable level.The beauty of this book however is that the exercises rapidly increase in punch, and I still return to it from time to time to tease out new relationships.

It's introduction to graph theory is also very stellar... and it decides to introduce it before the combinatorial arguments, which if I'd had a little stronger comp sci background before taking the class, I would have found a much more gradual introduction to the general theories.

I'm still raising in mathematical ability, and I plan on tackling this book when I've gotten a little more maturity under my belt.

Excellent book.Hands down. ... Read more

Product Description
This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items. ... Read more

Product Description
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest.

In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory.

In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader. ... Read more

Customer Reviews (5)

Bollobas
This is a very well structured book. However, this book is not amenable to easy reading. The theorem proofs are short and concise with no overt explanations. Bottom line is that reading this book is a an exercise for the brain.

Being an engineer my only grouse about this book is that this book is written for mathematicians and as the author himself claims there are very few practical applications accompanying the theory. But this being a graduate text in mathematics it really cannot be expected to fulfill this need.

I have so many good things to say about this book...
This book is absolutely precious!It is a little bit weird, but you can get used to it.This book's strongest points are that it is easy to jump around in it, and it contains a wealth of material.It also has incredible numbers of exercises, of greatly varying difficulty levels.

The author's clarity of writing comes out particularly well in the later chapters.In particular, my favourite parts are the discussion of algebraic graph theory, and the discussion of the Tutte polynomial and connections with knot theory.There is also some beautiful use of linear algebra in various parts of the book; some rather strange and difficult results are presented very clearly.

I think this book would be a great purchase for anyone wanting to engage in some self-study in graph theory, or anyone wanting a good reference on graph theory, or anyone wanting to work some hard problems (or easy problems) in graph theory, or someone choosing a textbook for a graph theory course...or...in short, anyone who wants anything to do with graph theory at all.

Good Introduction, too many typos
I am, what Prof. Bollobas would call a hobby mathematician. Some popular science book arouse my interest in graph theory, and the author of that popular science book recommended this book. I feel it was a vey good introduction to the subject, even though the proofs become challenging at times. His motivation for the subject is always concise but precise, one cannot but notice, that a master of the subject is writing about it.

The only distraction are the enormous number of typographical errors: I counted over 60, and this in a third corrected printing!?!

Excellent in content, but somewhat challenging in narrative
Bela Bollobas has the rare gift of having both deep mathematical insights, and the ability to eloquently communicate them in a way that is accessible to the average graduate student. In his book "Modern Graph Theory", Bollobas covers just about every exciting area of the subject, and does so in an up-to-date fashion that gives the reader a big picture of each sub-area of the field. The ability to do this not only seems difficult, but also essential, since he himself has written entire books on two of the chapters (extremal graph theory, and random graphs). Just about every major important theorem (including max-flow/min-cut Theorem, and theorems by Menger, Szemeredi, Kuratowski, Erdos/Stone, and Tutte) can be found here, and thus makes this book indispensable for anyone who does research in graph theory, combinatorics, and/or complexity theory.In my opinion the true highlights of this book are indeed those areas he knows best: extremal graph theory, random graphs, and random walks on graphs, the latter of which may be the best introduction to that subject that one will find in a textbook.

My only complaint, at the cost of perhaps half a star, is that his discussions and proofs often seem difficult to follow, as he will state something that to him seems quite obvious, yet to this reader often seemed a bit subtle, and would hence slow down the reading. Indeed, if these off-handed remarks were included as exercises at the end of each chapter, then the number of excercises would have swelled from the current 600 to well over one thousand ! Speaking of which, these 600+ exercises, although also representing another blessing of this book in that they add another degree of depth, tend to lack "starter" exercises, and go straight to the theory. But this is to be expected froma graduate text.

Finally, for the reader whose research significantly intersects with graph theory, but may not be ready or willing to be initiated by Bollabas into the world of graph theory, I would recommend Dietsel's graduate text on the subject. His book covers similar topics, but may be more clearly and transparently, but with less depth and insight.

A good introduction book
My profile is the following: I am a phD student in theoretical computer science and I needed a good introduction book to graph theory.

This book is just what I needed... ... Read more

Product Description

Customer Reviews (1)

A book on graph theory
Pearls in graph theory begins informally and at an elementary level, suitable for a substantial freshman-sophomore course. After intuitive introductions, concepts and theory are developed with increasing depth, leading into material for a good intermediate-level course. Included also are appropiate open conjetures on, for example the Oberwohlfach problem, magic and antimagic graphs, and colorings of "earth-moon" maps. In addition, for me the final three chapters are asplendid, enticingly elementary yet comprehensive introduction to topological graph theory. Essentially no othr introductory text presents thedepth, breadth, and fun of topological graph theory as does this book. ... Read more

Product Description
Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher--one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics. ... Read more

Customer Reviews (3)

The secret of the Laplacian
This book is intended for the professional mathematician that want to learn about the misteries of the eigenspectrum of the graph laplacian.

A lot of misteries, a lot of fun.

Less than or equal to
I found some very good stuff in this book.
It is buried deep though.
Again Fan Chung writes a book on graph theory with
just about no simple examples or graphs at all.
The Cheeger constant and, both the volume and diameter measures
are not presented in an accessible way: just no real way to
calculate them is given.
What is important seems to be what isn't mentioned anywhere:
the Cartan, Dykin andCoxeter approach to graphs and large scale symmetry.
The treatment of the buckyball is the one concrete example and
the results instead of being explain are just given
without sufficient explanation.
I have also to review Fan Chung's 2006 lecture with Linyaun Lu Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics) which appears to be a little better written.
Some one seem to have told Fan Chung that proofs with less an or equal to are O. K.: they are in most cases a bad mistake in a book such as this for graduate students.

Elegant and coherent, but a bit dry and unmotivated
This book is elegant and accessible, with a coherent presentation, but is a bit dry and unmotivated. The book would benefit from more applications, which should not be hard to find. I felt like Chapter 8 was the high point of the book, with a discussion of random walks, a matrix-tree theorem and invariant field theory.

The researcher who needs an arsenal of technical results in a clear style will find it here; the student who desires some added perspective may come away somewhat dissatisfied. ... Read more

Product Description
Never HIGHLIGHT a Book Again!Virtually all testable terms, concepts, persons, places, and events are included. Cram101 Textbook Outlines gives all of the outlines, highlights, notes for your textbook with optional online practice tests. Only Cram101 Out ... Read more

Product Description

Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus, in that it combines the features of a textbook with those of a problem workbook. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed, and reinforced by working through leading questions posed in the problems.

Customer Reviews (1)

As a text in graph theory, it will work for some but not for others
While this book could be used as the text in a course in introductory graph theory, to do so will likely require additional effort on the part of the instructor. Outside of the definitions, there is very little in the way of explanatory text. Once the definition and any relevant theorems are given, the author goes directly into the problems over that topic. The majority of the pages are devoted to problems and solutions to some of them are included.
Most students will not be able to make the leap directly from the definitions to the problems, although with motivation and some effort many will be able to perform the transition. Part of the problem will be due to their most likely not having been exposed to this approach before. The fundamental tactic used in the foundation classes of calculus and linear algebra is to have some explanations followed by several worked examples and this is a definite change.
If you are willing to work through some of the example problems with the students, then this will be an excellent textbook for a course in fundamental graph theory. The coverage is complete and there is an abundance of problems that can be worked. However, if you or your students are much more comfortable in having a great deal of explanations in the text, then you will find this one lacking.
... Read more

Product Description

Far more "user friendly" than the vast majority of similar books, this volume is truly written with the unsophisticated reader in mind.  The pace is leisurely, but the authors are rigorous and maintain a serious attitude towards theorem proving throughout. Emphasizes "Active Reading" throughout, a skill vital to success in learning how to write proofs. Offers two sections on probability (2.4 and 2.5). Moves material on depth-first search, which previously comprised an entire (very short) chapter, to an earlier chapter where it fits more naturally. Rewrites section on RNA chains to include a new (and easier) algorithm for the recovery of an RNA chain from its complete enzyme digest. Provides true/false questions (with all answers in the back of the book) in every section. Features an appendix on matrices.  A useful reference for mathematics enthusiasts who want to learn how to write proofs.

Customer Reviews (14)

Horrible!!!!
The concepts taught in this is fairly straight forward, but the Author makes every attempt to confuse and make it difficult. I have never seen such a horrible math book in all of my years as a student. I'll break down a typical chapter:

Chapter organization (i.e. are the topics covered related?): Pretty good as as whole. Each topic is introduced bit by bit and the flow from one section to the next makes sense.

Each individual section:

Each section and chapters too, are prefaced with some nonsensical garbage that kind of relates to the chapter; sometimes it's some stupid fictional story the author wish would happen with his fictitious friends, and other times it would be a situation that could maybe might happen in real life, assuming you're a total loser, and have nothing better to do than to count things. Or maybe you're the count, from Sesame Street. I don't know, whatever.

Then the author introduces the concept, and makes it has hard as possible to get and understand.

After that, he has 'Pauses' where you're suppose to suddenly understand what he's suppose to be teaching you. These pauses make no sense, and might as well be at the end of the chapter or section.

The book does do a decent job in highlighting key concepts and definitions, but I still find some important information and key concepts buried deep in some example.

After that, you may still be wondering why this book is not even worth 1 star. This is why:

Proofs are INSANELY hard to flow.
Examples are also INSANELY hard to flow.
That's because the author thought it would be best solve the problem as if he's talking you through it. The only way he can do this is by putting the BOTH proofs AND examples in a paragraph INSTEAD of showing the steps LINE BY LINE. Every good math book worth its salt has the examples shown clearly line by line. They may never show every obvious step they make, but it's at least easy to see what you understand and what you don't understand. This book uses one paragraph to explain the answer. And it's not even a long paragraph. So this MATH book ends up being a wall of text. Most of the symbols are just bold alphabet charaters, so it makes it even harder to find what you're looking for and follow the text.

What broke the straw on the camels back is the fact that his text is setup like this: (periods added for clarity)
Example 11: BLAH BLAH BLAH BLAH BLAH
............BLAH BLAH BLAH
............_______________
............ Problem 12: Stupid problem here.

I am not sure what the difference is between Example and Problem, but he uses PROBLEM to describe an example and exercise to describe the problems you're suppose to work out. Then occasionally he will have an 'exercise' refeer to a 'problem' and you looking at the wrong thing for five minutes before you realize. Also he will do this:

problem 12 blah blah blah sets up problem whatever.
...refeer to exercise 32 for more.

Of course, the exercise doesn't have the answer, and they just say 'work problem 12 blah blah'. But then puts the answer in the back of the book.

Overall this book is extremely terrible, and you should shame your professor if he tells you to buy this god awful book. If your professor tells you to buy this book, then he probably also sucks at teaching the material, and I would strongly consider dropping the class.

Not the best book for Discrete Mathematics
I have used this book for my Discrete Math class.

Pros: Has a lot of Exercises to work on. Pretty Advanced style of Explanation.If you have a good professor this book will help.

Cons: If you are just starting to learn Discrete Math, this is not the book for you. The examples and the explanation are pretty advance sort .
It is hard to understand Discrete Math byreading this book only .So if you are depending on your self i would suggest you look for a different book.

Gerry
This book is the worse math textbook I have ever encountered.There is not enough explanation regarding the theory and the examples are not helpful.The exercises in each chapter can not be referred back to the chapter reading at all.The chapter pages are structured to save paper.Everything is jammed together.I am currently taking the course and between the instructor and the book little knowledge is being passed to the less than ten people in the class.This book should NEVER be used!

Accessible, Friendly
I'm currently taking a Discrete Math class with this textbook.I don't have any background in the subject, and my theoretical math background is limited to a Proofs course and a Non-Euclidan Geometry class.(Other than that I have the usual amount of undergraduate calculus and so on.)

I think this book is fantastic.It is written in an engagingly casual style, and it uses a lot of examples and detail to work out the material.The other theoretical math texts I've used really don't do this - they expect you to treat their material more as hints to do your own work, which can be really hard for students (and is why you have a professor, after all).

I can't address how well this book actually covers the various topics of discrete math, since I only know what I've learned in the course so far, but I'm very impressed with how well it spells things out.It's not exactly "light reading" (it's not Discrete Math for Dummies) but it is quite accessible.

Discrete? More like hidden and vague...
I do not recommend this book. While yes, it provides clearly marked definitions and formulas, when giving examples, the work shown leaves out some key steps that leave the reader grasping into thin air trying to figure out the method to their madness. Some exercise questions are vaguely written, leaving the student to interpret the meaning, which may result in differing answers.

If you have a teacher who uses this book, get it. Otherwise, if you are teaching yourself (or just have that bad of a teacher), either pass on buying this book or buy a supplement. Or find a good math tutor, you'll need it. ... Read more

Product Description
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity.An effective use of examples, and huge number of interesting exercises, demonstrate the topics oftrees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs.For those who need to learn to make coherent arguments in the fields of mathematics and computer science. ... Read more

Customer Reviews (16)

As textbooks go, not bad.
This is the first Graph Theory book I've read, as it was assigned for my class.Therefore, I don't have an expansive frame of reference to tell how this comares to other textbooks on the subject.

However, I don't quite unerstand the frustration of many here.I'm assuming many had the first edition of the book, which was apparently rife with many errors.I personally only found one error in one of the proofs, and I'm still not certain whether it was actually an error or a misreading.This does coincide with one of the criticisms of the book, in which many of the proofs are very hard to follow, sometimes needlessly so.It would have been a lot easier to do the proofs in more of a bullet point fashion as opposed to several long, descriptive sentences.

The problems were very good, with a range of challenging to bash your head on the desk difficult.There were plenty of examples strewn over the text, especially for the more complicated proofs.

The range of data to tear through is formidible.This touches on all the important sections of Graph Theory as well as some of the more obscure uses.Lond story short, if this is your assigned textbook for a class, it's not half bad.I could have probably understood most of what was taught in my class by reading the book, but would certainly be no expert, so it's a relatively solid academic work.

Bad textbook
I had to purchase two of Prof. West's books.This one and the Mathematical Thinking book. Prof. West is not very competent in writing textbooks.He gives incomplete explanations of the very basic terms. His path to explain simple things to hard things is usually very random with completely random thoughts and observations in the middle of explanations (sometimes this creates a problem because you cannot always see "them" as a beginner). His explanations and proofs lack one thing that mathematics always preaches: parsimony, clarity, and elegance. Even his colleagues at UIUC criticizes the way he writes textbooks. If you are new to graph theory and if you buy this book, you'll definitely need to check definitions and explanations from either another textbook or from the Internet. He makes a mess out of the subject matter he is trying to introduce.I would not recommend this book at all.

Not bad
We used this for a Computer Science class on Graph Theory, and I remember more than one student complaining about the book. Generally speaking, what people found most disconcerting about the text was its level of abstraction, and "lack of motivation" for the theorems provided. In my experience, these complaints are frequently leveled by non-mathematicians at books that are clearly NOT non-mathematical; West's book falls into this category. This is, first and foremost, a book for mathematicians.

As pointed out by other reviewers, the book isn't perfect. There are a lot of errors, although you can obviously deal with these if you read the errata. West also has the habit of sometimes presenting a theorem completely out of the blue, which can cause some confusion. That said, the book does a very good job overall. Graph theory is an exceptionally beautiful subject, but it's easy to obscure that in a theorem/proof/theorem didactic haze. West has an agenda, and therefore the book has a discernible structure, which brings out the beauty of the area. The chapters on coloring and planar graphs are particularly strong, although the most interesting chapter for me was the one on additional topics; the sections on matroids, Ramsey theory, random graphs and spectral graph theory, while far from comprehensive, provide good introductions. Another strong aspect of the book are the exercises; these range from very easy to very difficult, the latter being from major papers in graph theory. The hints section at the end of the book is quite helpful here.

Overall, a very good book. I didn't know anything about graph theory before I started reading it, but I had a professor to help me through the rough spots, so perhaps it's not exactly ideal for self-study. If you've been exposed to the basics before though, it's definitely worth taking a look at.

Good middling book
The treatment is logically rigorous and impeccably arranged, yet, ironically, this book suffers from its best feature: it is comprehensive. As a book becomes more encyclopedic, it becomes less useful for pedagogy. Introduction to Graph Theory is somewhere in the middle. It is an adequate reference work and an adequate textbook. Steering a middle course, the book is bound to dissatisfy people with specific needs, but readers needing both a reference and a text will find the book satisfying.

If you buy it for pedagogical purposes, be prepared to consult other works for a more intuitive approach. Introduction to Graph Theory presents few models, relying instead on logically rigorous development. Personally, I'm for both, but that takes up space, meaning less material can be covered.

I'm glad I bought the book, and I will keep it for a future reference.

Graph lovers' book
West is enthusiastic about graph theory.I do not recommend this book for independent study, nor would I recommend it for a first-time student of graph theory.It is called "Introduction to Graph Theory", not because it is an appropriate introductory text for new students, but because it covers a broad area of the subject.I recommend it for a student who has read at least one lower-level introductory text and would like to round out their knowledge of graph theory in a more in-depth way.
I have two problems with this book.They both stem from the fact that it reads more like a collection of journal articles than like a cohesive text book.One is that his notation is very specific--he does not always use the most common form of notation, and this means that dipping into the book is difficult.The second problem for me is that West defines many things that I do not feel need defining.Rather than using a short description of a certain type of graph whenever he refers to it, he will give it a label.Again, this makes dipping into his text rather difficult, especially since many of the things he defines are not generally given a definition.Both of these would be perfectly reasonable for a journal article, but seem rather out of place in a large textbook--his definitions particularly clutter up his work.Perhaps West is more used to writing papers than textbooks.
Having said that, West is very knowledgeable and enthusiastic.His exercises are wonderful, marked with a (-) for easy, a (+) for difficult, a (!) for particularly instructive, and a (*) for problems based on optional material.Several of the (!) problems I have worked required me to actually look up the paper that they are based on for the final solution--which is possible due to his excellent citations.His index of works cited is an education in itself, and any student wishing to pursue a specific area in greater depth will find his book an wonderful gateway.

My perspective: I am an undergraduate student doing summer research in graph theory, working under a professor. ... Read more

Product Description
Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. An important part of learning graph theory is problem solving; for this reason large numbers of examples, problems (with full solutions) and exercises (without solutions) are included. Accompanying the book is a CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up to seven vertices, and a Graphs Editor that enables students to construct and manipulate graphs. Both the Database and Editor are simple to use and allow students to investigate graphs with ease. Computing Notes and suggested activities are provided. ... Read more

Product Description

The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.

Customer Reviews (4)

Nice introduction Graph Theory
Regardless some background topics are not covered, I see NO LACK of mathematical strictness, but authors use many didactic tools to reaffirm readers understanding --expand topics on appendices many drawings, many examples, and exercises on the end of each topic. Mathematical notation is used in the way it is needed, to grant it will not confuse reader, a post-appendix topic is reserved to explain mathematical notation, it includes general mathematical notation, structures, operations and relations, graph parameters, family of graph, and others.

As the book series indicates, it is targeted to those whose are mathematical ripe to understand theorems and its proofs. Its references includes great papers and academic works. Asserting their authority in Graph Theory, pay attention to authors mentors: Claude Berge, Paul Erdös, and Bill Tutte.

I used this book a year from the library, and I'm buying it. An introductory course could safely use it, combined with "Graph Theory: Exercises book" (Lovasz), and "Algebraic Graph Theory" (Godsil & Royle).

Excellent book
The book from the seller was in great shape and unlike some sellers, was shipped in time anthe product particularly was in mint condition

Graph Theory Book
The book was in perfect condition. It got here promptly, and I am very pleased with my purchase.

excellent
i found that this book is excellent , espicially for those who want in the future to go deeply in their research
... Read more

Product Description
This is a companion to the book Introduction to Graph Theory (World Scientific, 2006). The student who has worked on the problems will find the solutions presented useful as a check and also as a model for rigorous mathematical writing. For ease of reference, each chapter recaps some of the important concepts and/or formulae from the earlier book. ... Read more

Product Description
Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates.Much care has been given to present the material at the most effective level for students taking a first course in graph theory.Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet accessible text that stimulates interest in an evolving subject and exploration in its many applications.

This text is part of the Walter Rudin Student Series in Advanced Mathematics. ... Read more

Customer Reviews (2)

Good for independent study.
I'm yet to take a course on Graph Theory, but this book was clear enough that I was able to get started on my own.

An excellent text
This textbook was such a great complement to the course I took in Graph Theory.Everything is explained beautifully, from simple things such as definitions of elementary terms to subjects more complex such as the coloring theorems of Vizing and Shannon.Proofs accompany nearly all theorems/conjectures in the book, and they are done in a clear and concise manner.What I also found particularly interesting were the various historical pieces that the authors added to the book.They are not only interesting but they serve as a nice break between sections of purely technical content.

This is a great text to have on hand for an introductory course and I highly recommend it for anyone looking for such a text. ... Read more

Product Description
Already aninternational bestseller,with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety ofcourses -- a textbook that will continue to serve your students as a reference for years to come.

The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.

What else is new?

Customer Reviews (7)

great and comprehensive book on graph theory
This is a great and comprehensive book on graph theory. The book can also serve as a reference. It is well-written, clear and precise. Almost everything that a student or practitioner need to know about graphs is likely to be found here. However the book is best appreciated by someone who has studied some graph theory. A beginner would benefit more by looking at more elementary books such as Graphs and Applications by Wilson.

Horrible textbook
Reads like a dictionary, each page is nothing more than bullet points that alternate between definitions and corollaries.Proofs are typically very short: explained and illustrated in no more than a quarter of a page.More appropriate as a reference manual than a textbook for a class.

Plain and simple: EXCELLENT book

This is a superb book for an introduction to graph theory. It is not just a pile of theorems as other books you'll find in this field. It presents insight and intuition first, and then it gives the necessary formal treatment. The topics covered are perfect, in the right order.Extremelly recommended for anyone eagerly wanting a first contact with this exciting field, as well as for any graph theory instructor looking for the right book to follow in class.

great, comprehensive introduction
Regardless of whether you just want to implement a couple of graph algorithms or get into the guts of graph theoretic proofs, this book should come in as a great resource.

In over 500 pages, this book covers a lot of ground beyond the basics, such as topology of graphs, graph operations and mappings, voltage graphs, and surface imbeddings.Definitions are very clear, propositions and proofs are stated very clearly, and there are shrink-wrapped algorithms if you just want to apply them.

Requiring no previous knowledge of abstract algebra or graph theory, this is a great resource to have in your bookshelf.

not recommended
This book was used for my undergraduate course in introductory graph theory, which was split between math and computer science students. I found that this book left to be desired. The definitions are imprecise and often inconsistent with those that are standard, and much of the notation used is not standard. I would not recommend this book as a reference or for advanced students. ... Read more

Customer Reviews (2)

Excellent for a first course
This is a great book. It's supposed to be used in a first course in Graph Theory; so don't worry if it doesn't cover everything. It's supposed to be basic (but that does not mean it isn't rigorous!). It's a joy to read, and is (in my opinon) the perfect choice for a one-semester undergraduate course (for Math or Computer Science majors).

a classic book
This is a classic book on graph theory. However, it's quite outdated and is superseded by the author's new book. Now this book can be downloaded from the author's website for free. ... Read more