Product Description

Once considered an “unimportant” branch of topology, graph theory has come into its own through many important contributions to a wide range of fields – and is now one of the fastest-growing areas in discrete mathematics and computer science. This practical, intuitive book introduces basic concepts, definitions, theorems, and examples from graph theory. Presents a collection of interesting results from mathematics that involve key concepts and proof techniques. Covers design and analysis of computer algorithms for solving problems in graph theory. Discusses applications of graph theory to the sciences. Includes a collection of graph algorithms, written in Java, that are ready for compiling and running. For anyone interested in learning graph theory, discrete structures, or algorithmic design for graph problems.

Customer Reviews (1)

Good Introduction
This is a very good introductory book on Graph Theory. If you don't want to be overwhelmed by Doug West's, etc., and yet receive a decent introduction to the topic, this book is your best bet. It covers all the topics required for an advanced undergrad course or a graduate level graph theory course for Math, engineering, operations research or computer science students in good depth and details. There are good examples and interesting exercises; some computer codes (JAVA) are also available in the book implementing some of the algorithms.
I would say O.R. and CS people will benefit a lot from it both as a reference or a textbook if adapted for a one semester graduate course. The only drawback is the price!
... Read more

Product Description
Line graphs have the property that their least eigenvalue is greater than or equal to -2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. The authors discuss the three principal techniques that have been employed, namely 'forbidden subgraphs', 'root systems' and 'star complements'. They bring together the major results in the area, including the recent construction of all the maximal exceptional graphs. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. This will be an important resource for all researchers with an interest in algebraic graph theory. ... Read more

Product Description
Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications.Key features:* Introductory chapters present the main ideas and topics in graph theory—walks, paths and cycles, radius, diameter, eccentricity, cuts and connectivity, trees* Subsequent chapters examine specialized topics and applications* Numerous examples and illustrations* Comprehensive index and bibliography, with suggested literature for more advanced materialNew to the second edition:* New chapters on labeling and communications networks and small-worlds* Expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems* Many additional changes, improvements, and corrections throughout resulting from classroom use and feedbackStriking a balance between a theoretical and practical approach with a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites.-----From a review of the first edition:"Altogether the book gives a comprehensive introduction to graphs, their theory and their application…The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well… It is very useful that the solutions of these exercises are collected in an appendix."—Simulation News Europe ... Read more

Customer Reviews (2)

There are much better Graph Theory Books
The errors in this text are unfortunate, and the presentation is not engaging. I did find that "A First look at Graph Theory" by Clark and Holton was useful and "Introduction to Graph Theory" by Chartrand and Zhang, was very readable.

Affordable but not accurate
It's nice to have an affordable math book, and this one does give a good introduction to graph theory.Unfortunately, there are also mistakes (some of which REALLY should have been caught in proofreading) which could confuse someone attempting to learn graph theory from this book.(These are both in the text and in the answers provided for the problems, such as giving the wrong number for the length of a path) ... Read more

Product Description
With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material.The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica. ... Read more

Customer Reviews (3)

useful for who want to learn discrete mathematics with mathematica of Wolfram research software
though the program created more than 6 years ago, it's useful reference for learning discrete mathematics with mathematica software

Way too specialized to be a stand alone discrete math text
I think the best parts of this book was the illustration overleafs for each chapter. There are some pretty cool images created using Combinatorica and Mathematica. I got this book to help me with my Discrete math course and with that in mind it wasn't as helpful as I thought it would be. I think the reason is that it's really a book about Combinatorica and how to use it with Mathematica and how the latest version is faster and how the functions were written. So in order to use it effectively you have to already be quite familiar with discrete math and graph theory to use this. There are plenty of examples to try and play with though if you can get it to run. In Mathematica7 and I would get alot of this command is obsolete warnings or errors. The book website says they have an updated version of Combinatorica but I didn't try that. Also, there are some exercises but no answers provided for any of them. There is also a complete listing of all the Combinatorica in the book but no clear indication if it's now included with the latest version of Mathematica which would be helpful. I don't see how this book could be used as a primary text for a discrete math course unless you had an excellent instructor to add all the material the book is missing and to walk you though putting the example in the book to best use. This book will appeal most to those that use Mathematica with discrete math and find the documentation lacking or want to find out how the Combinatorica functions were programmed. If you are using it just to supplement a discrete math course as I did you probably won't benefit as much.
I must admit it was kind fun seeing Mathematica choke up on trying to spit out a 20x20 gridgraph! Never seen it do that before on my quadcore pc.

It fills a Mathematica niche to perfection
This book has two primary uses, as a reference for the Combinatorica extension to Mathematica or as a textbook in a course in combinatorics and graph theory where Mathematica is extensively used. In both cases it is the best resource on the market. Combinatorica is an extremely powerful package that allows for very sophisticated operations to be performed in combinatorics and on graphs. However, there is no coverage of other areas of discrete mathematics.
The structure of the book is that it is split up into sections. For each section, there is a short textual description of the operation, a section of code illustrating the appropriate function(s) and the output from that code. The output is sometimes in the form of a textual listing and at other times an actual diagram. A complete listing of the functions and their actions is given in an appendix.
While this book is not one that could be used in a general course in discrete mathematics, it is an exceptional example of one that fills a niche to perfection. If you have any interest in doing combinatoric or graphing operations with Mathematica, then you have to look no further.

Published in Journal of Recreational Mathematics, reprinted with permission.
... Read more

Product Description
From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1 ... Read more

Product Description
The fourth edition of this standard textbook of modern graph theory has been carefully revised, updated, and substantially extended. Covering all its major recent developments it 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.electronic edition: diestel-graph-theory.comFrom the reviews of the first two editions (1997, 2000):"This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory."Acta Scientiarum Mathematiciarum"The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory."Bulletin of the Institute of Combinatorics and its Applications"A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors." Mathematika". . . like listening to someone explain mathematics."Bulletin of the AMS ... Read more

Customer Reviews (8)

Dense reading
I have to read this book to prepare for a summer research program; however unfortunately for a high school student, this text is unreasonably concise with the proofs and makes for very tough independent study.

An exciting book.
Really, this book is very nice. It is simple to read (its language is quite easy) yet serious and precise. It covers many important aspects of the pure graph theory , leaving there applications and algorithms to an algorithmic graph theory book. So, to learn the core of the pure graph theory, this book is your choice, espesially if you are a computer science student (Because it dosen't deal deeply with tough mathematics).

Small yet comprehensive.
An excellent book. With minimum knowledge and an open mind, you can work rapidly throughout this book. I used it as a reference for some work I'm currently doing on the structure of extremal graphs and it came in very handy. To sum up, it's what you would normally expect from Springer's series on grad math texts.

A class for theoretical math, but not applied math
I used this text in school, as a computer science student in a theoretical math class.

If you are looking for examples of computer algorithms, look elsewhere; the closest this will get you is to "existence proofs", which is showing that something (such as a hamiltonian cycle) exists in a graph that has thus-and-such number of points or edges, but not tell you which sequence of points/edges make up that something. (For example, a graph can be embedded in a plane unless there's a subgraph that looks like K(5) or K(3,3) inside it - this is in about chapter 5, and an important theorem. The text proves this, but doesn't tell you HOW to embed the graph in a plane.)

That said, this is an excellent book for theoretical mathematics. I understand that the first two chapters can be used as a high school math text, as an introduction to proofs, and agree that it would work well.

As a formal introduction to proving theorems, especially in a self-contained world (you don't need many prerequisites for this, like you do for a topology or analysis text), this is pretty swell.

So, to the person who said that he didn't like this because there weren't algorithms in the book: you can find those in the semiliterate computer science textbooks. (I would insist that the last four words of the previous sentence are redundant.)

Look here for mathematics.

Exellent Introduction
Almost no pre-requisites are needed for this book, (There is a shortsection which touches on Linear Alg, and another on very elementarytopology) and yet it will take you from the very basic notions, to researchlevel problems in this subject. It covers almost all the major notionsabout graphs, including coloring, matching, flows... Any reader is bound tofind the section on Ramsey theory especially interesting. However, infinitegraphs and Algebric graph theory are not covered.

There is a usefulcommentary on the references at the end of each chapter. ... Read more

Product Description
This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalization of Part I.The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph coloring. The second part considers generalizations of Part I and discusses hypertrees, bipartite hyper graphs, hyper cycles, chordal hyper graphs, planar hyper graphs and hyper graph coloring. There is an interaction between the parts and within the parts to show how ideas of generalizations work. The main point is to exhibit the ways of generalizations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hyper graphs.This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hyper graphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view. ... Read more

Product Description
William Tutte, one of the founders of modern graph theory, provides a unique and personal introduction to the field. Instead of a typical survey, the author looks back at the areas which interested him most, discussing why he pursued certain problems and how he and his colleagues solved them. The book's extensive references make it a useful starting point for research as well as an important document for anyone interested in the history of graph theory. The author begins with the problems he worked on as an undergraduate at Cambridge and goes on to cover subjects such as combinatorial problems in chess, algebra in graph theory, reconstruction of graphs, symmetry in graphs, and the chromatic eigenvalues.In each case he mixes fascinating historical and biographical information with engaging descriptions of important results. ... Read more

Customer Reviews (2)

An introduction to some advanced theorems on graphs
The author has spent most of his professional life pondering some of the more substantial problems in graph theory. This book is not a comprehensive treatise on the subject but an organized collection of a series of lectures that he delivered in 1984. The lectures were just as much an attempt to provide insight into the process that led to some advanced theorems as about the theorems themselves. For this reason, the book is best suited for the beginning graduate student with some experience in the field.
Some of the problems covered in the book are: the knight's tour problem as an exercise in graph theory, subgraphs and Hamiltonian circuits; algebra in graph theory, symmetry in graphs and graphs on spheres. Throughout the explanations of the problems and the solution strategies, it is impossible not to appreciate the effort that was put forward to solve them. Tutte is clearly one of the leading authorities in graph theory and good at explaining what graph theory is all about.
This is not an easy book to read, yet it is readable. It would be ideal as the material for a graduate seminar in graph theory or a text in advanced topics.

Inside the mind of a great mathematician
It is unquestionably that W. T. Tutte is today one the greatest mathematicians in the world. I read this book with great enthusiasm because the author explains, with the work that made his fame, the most difficultpart of the discovery of mathematics: The creativity involved.

Thestudents will find in this book a great motivation to thinking inmathematics. For the experimented mathematician this book will make clearthe born procces of some classic results in graph theory.

This is anexcellent book, is just the story of a life of work and fun. ... Read more

Product Description
From specialists in the field, learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course. ... Read more

Customer Reviews (2)

Cartesian-product graphs: state-of-the-art + many exercises
In the book Product Graphs: Structure and Recognition (Wiley-Interscience Series in Discrete Mathematics and Optimization) by Wilfried Imrich and Sandi Klavzar, published in the World Mathematical Year 2000, the main results on the structure and algorithmic properties of the four principal graph products (Cartesian, direct, strong, and lexicographic) were brought together for the first time. Now the authors have joined forces with Douglas F. Rall in a new book. All three authors being among the leading researchers in the area of graph products, it is not surprising that the new book contains many state-of-the-art results which appeared in scientific journals at about the same time as this book was published. Even before its release the book was thoroughly tested in several graduate-level courses at the authors' home universities.

The thread of the book are Cartesian products of graphs and their subgraphs, which - due to their nice metric properties - have numerous applications in coding theory, radio-frequency assignment, theoretical chemistry, etc. Following this thread, the reader encounters all the principal areas of graph theory: from connectivity, hamiltonicity and planarity, through different invariants, to the metric, algebraic and algorithmic aspects of graphs. The book is divided into five main parts and 18 chapters. The average length of a chapter is below ten pages which makes the book accessible also to the less experienced reader. Another praiseworthy feature are the "trailers" at the start of each chapter which give a short preview of the chapter and place it in the broader context.

In part I we learn the definition and the basic properties of the Cartesian product of graphs. We also meet some important families of graphs which are either defined or characterised in terms of the Cartesian product, such as the hypercubes (= Cartesian powers of the complete graph K2), Hamming graphs (= Cartesian products of arbitrary complete graphs), and Hanoi graphs (= spanning subgraphs of Hamming graphs, describing the state space in the well-known Tower of Hanoi problem).

Part II discusses hamiltonicity, planarity, crossing numbers, connectivity, and subgraphs, first in general, then in Cartesian-product graphs. The still-open 1973 conjecture of Rosenfeld and Barnette that a prism (= Cartesian product with K2) over any 3-connected planar graph is hamiltonian is stated, and an elegant proof of the theorem that the k-tuple prism (= Cartesian product with K2^k) over such a graph is hamiltonian for all k >= 2 is given.

Part III investigates graph invariants such as independence number, chromatic number, P-chromatic number (where P is some hereditary property of graphs), circular chromatic number, list chromatic number, L(2,1)-labeling number, chromatic index, and domination number. The authors study the question of what can be said about the value of a certain invariant of a Cartesian product provided that one knows its values on the factors. As we learn, the answers can differ widely for different invariants. For example, while it is relatively easy to see
that the chromatic number of a Cartesian product equals the largest chromatic number of its factors, the 1968 Vizing conjecture stating that the domination number of a Cartesian product equals or exceeds the product of domination numbers of its factors is still open.

As already mentioned, the widespread applicability of Cartesian-product graphs stems primarily from their nice metric properties; these are the subject of Part IV of the book. Here the authors show that the diameter resp. the radius of a Cartesian-product graph equals the sum of the diameters resp. the radii of its factors, and that its Wiener index (a number used in theoretical chemistry to describe certain physico-chemical properties of molecules) can be easily computed from the corresponding indices of its factors. Among the subgraphs of a Cartesian-product graph G, special attention is devoted to the isometric subgraphs whose metric agrees with that of G restricted to the vertex set of the subgraph. So, for instance, partial cubes are the isometric subgraphs of hypercubes, and partial Hamming graphs are the isometric subgraphs of Hamming graphs. This part of the book ends with a proof of the Fundamental Theorem of the metric theory of Cartesian-product graphs which says: Every graph has a canonical metric representation, i.e., a unique isometric embedding into a Cartesian-product graph with maximum number of irredundant factors.

Part V of the book surveys algebraic and algorithmic aspects of Cartesian-product graphs. The set of all graphs (with isomorphic graphs identified), equipped with the operation of Cartesian product, is an abelian monoid. In analogy to prime numbers, those graphs which do not possess a non-trivial Cartesian-product factorization are called prime graphs. The authors show that unique factorization into prime graphs holds for all connected graphs, while disconnected graphs may have several distinct such factorizations. Therefore it is quite surprising that the cancellation property, as well as uniqueness of r-th roots, hold for all graphs. Using uniqueness of factorization into prime graphs, the authors determine the structure of the automorphism group of a connected Cartesian-product graph: it is isomorphic to the group of automorphisms of the disjoint union of the prime factors of the graph. Then they use these results to analyze the distinguishing number of a graph, i.e., the least natural number d such that there is a labeling of the vertices with d labels, preserved only by the identity automorphism. In this way they prove that the distinguishing number of the k-th Cartesian power of any non-trivial connected graph, different from K2 and K3, equals 2 for all k >= 2. In the last chapter of the book, the authors present two important algorithms: for factoring a connected graph into prime graphs, and for recognition of partial cubes, both with time complexity O(m n) (where n is the number of vertices and m the number of edges of the given graph).

An especially valuable part of the book are the more than 200 exercises which conclude every chapter. For each of the exercises either a full solution or at least a hint is provided at the end of the book. The list of 122 references is followed by the name, symbol, and subject indices.

Researchers in graph theory will find in this book an encyclopedia of known results on graph products, and teachers will welcome it as an excellent textbook. It will also be enjoyed by all other devotees of graph theory who wish to learn the state of the art in this area.

A quarter of the book is dedicated to exercises and their complete solutions
There's more to graphs than the average person would ever know. "Topics in Graph Theory: Graphs and Their Cartesian Product" is a scholarly textbook of graph theory; a quarter of the book is dedicated to exercises and their complete solutions. Chapters cover Cartesian products, more classical products such as Hamiltonian graphs, invariants, algebra and more. "Topics in Graph Theory" is an ideal text for classroom or self-study.
... Read more

Product Description
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as "pure" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to find and easy to understand. The treatment of each topic includes lists of essential definitions and facts accompanied by examples, tables, remarks, and in some areas, conjectures and open problems. Each section contains a glossary of terms relevant to that topic and an extensive bibliography of references that collectively form an extensive guide to the primary research literature.The applications of graph theory are fast becoming ubiquitous. Whether your primary area of interest lies in mathematics, computer science, engineering, or operations research, this handbook holds the key to unlocking graph theory's intricacies, applications, and potential. ... Read more

Customer Reviews (2)

Comprehensive supplementary reference
Don't try to learn anything for the first time from this. In each of the book's 54 sections, information is delivered as bulleted lists of definitions and theorems (called "facts") and there are extensive references to the literature. To maximize brevity, there is seldom any narrative introduction and only a few brief examples. No proofs, just references to them.

I noted two significant gaps in coverage. Since the main application of graph theory is in computer science, much of the Handbook relates to that field, yet there is no chapter on computational complexity. The other absent topic is scale-free graphs.

Nothing more than a handbook
As the title indicates, this is not a textbook, but a handbook. Theinterest of this one is to have pointers to the literature and to cover as much as possible of graph theory, so don't expect to find much details about something particular. I don't think it's useful for anything else than having a "close to hand" access to most of graph theory, hence only three stars for this limited interest compared to the relatively high price. ... Read more

Product Description
This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science.Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. This approach allows to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks.In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, peer-to-peer systems, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they:1.Have learned how to read and understand the basic mathematics related to graph theory.2.Understand how basic graph theory can be applied to optimization problems such as routing in communication networks.3.Know a bit more about this sometimes mystical field of small worlds and random networks.There is an accompanying web site www.distributed-systems.net/gtcn from where supplementary material can be obtained, including exercises, Mathematica notebooks, data for analyzing graphs, and generators for various complex networks. ... Read more

Product Description
There are several books on the applications of graph theory, but none of them are related to power systems applications. This book attempts to cover all applications of graph theory in the area of power systems. It consists of two parts. The first part, containing four Chapters, briefly introduces the basic concepts of graph theory, major properties, theorems, and algorithms in graph theory and network flow programming. This definitive treatment makes graph theory easy to understand. The second part, containing 10 Chapters, is the practical application of graph theory and network flow programming to all kinds of power systems problems, which is the key part of the book. These applications include network flow calculation of power flow, classical economic power dispatch, security constrained economic dispatch, multi-areas system economic dispatch, reactive power optimisation and pricing in multi-area environment, hydro-thermal power system operation, power system state estimation, secure economic automatic generation control, automatic contingency selection, distribution network optimisation, and optimal load shedding.The treatment of each application includes the mathematical representation of power system problem, its relationship with graph theory and network flow programming, as well as the implementations accompanied by examples of power system application problem, solution, and results analysis. Each chapter contains the related references that collectively form an extensive guide to the primary research literature. ... Read more

Product Description
This volume covers the principal branches of graph theory inmore than a thousand exercises of varying complexity. Each sectionstarts with the main definitions and a brief theoretical discussion,which will serve as a reminder when solving the problems. Answers andhints are supplied separately. Topics include trees, independence andcoverings, matchings, tours, planarity, colourings, degree sequences,connectivity, digraphs and hypergraphs.
Audience: This work will be valuable to researchers, lecturersand graduate students in graph theory, combinatorics, VLSI design,circuits and systems, and mathematical programming and optimization. ... Read more

Product Description
In 1736, the mathematician Euler invented graph theory while solving the Konigsberg seven-bridge problem. Over 200 years later, graph theory remains the skeleton content of discrete mathematics, which serves as a theoretical basis for computer science and network information science. This book introduces some basic knowledge and the primary methods in graph theory by many interesting problems and games. ... Read more

Product Description

Customer Reviews (1)

Not amused
I strongly suggest avoiding this book until the authors produce a more readable/useable next edition.Or else just go find an alternative book. The subject matter is quite interesting and useful but the book makes it extremely difficult to learn. For the sake of definiteness I will provide a technical example without defining terminology: There is a figure 3.5 on page 41 which shows a planar graph and its abstraction into a "PQ-tree", containing P-nodes and Q-nodes. P-nodes are cut vertices in Bk and Q-nodes are 2-connected components of Gk. Bk is shown in the figure, as is the PQ-tree. Gk is not shown but aside from the virtual vertices it ought to correspond to Bk. The problem is that Bk clearly has two cut vertices whereas only one cut vertex is represented in the PQ-tree as a P-node. So there is obviously a missing piece of information: How does a Bk cut vertex get translated into a Q-node 2-connected component of Gk? It is at best incomplete and confusing, at worst just wrong. This is not the exception: it is the rule for how the book is written. Only by re-re-re-reading sections and filling in omitted details does one arrive at what the authors should have said. This is not clever. This is not "economical writing". This is wasting the reader's time making the subject unnecessarily difficult. If I were to peer-review chapters 1 through 3 of this book for a journal article I would recommend Do Not Publish Without Major Revisions. I appreciate that the authors started to write this book; they just need to finish it, please. ... Read more

Product Description

Customer Reviews (1)

Trying too hard to mathematicize the social sciences
In the early '70's I took a course in sociological research methods that was organized around this book and included unpublished material by Harrison White as ancillary reading.The theory of directed graphs is as abstract and difficult as most other forms of mathematics, and the book is remarkably short on concrete applications to discerning the structural character of organized social settings.

Though the book was published in the mid-'60's, most of the end-of-chapter citations are from the '40's and '50's.At the time I read it, I got the distinct imprssion that the theory of directed graphs had been investigated in preceding decades and was found to lack promise for sociological research.

The instructor who taught the course was very good at working with this material, and I recall him solving a problem pertaining to identification of social roles using data collected in a monastery, replicating an analysis reported by White and one his graduate students.The solution seemed to make sense, but its value struck me as alarmingly dubious.When I gave voice to my reservations, I was advised by the instructor, as well as some of the other students in the class, that I might not be well-suited for a career in sociology, and they were right.

Nearly forty years later, the theory of directed graphs and related topics in mathematics are still studied by social scientists, and still provide challenges for sociologists with an apitude for mathematics.Harrison White, moreover, has become an influential social theorist, based largely on his work in social network analysis, an enedavor that is informed heuristically by graph theory but leans most heavily on computational alorithms that cumulate interaction patterns, thereby defining the location of each entity relative to all others.

Though the concepts "graph theory" and "social structure" share an intuitively appealing ring, it's not at all evident that the joining of the two has substantially improved our understanding of the organization of social life.This judgment may reflect my lack of interest and advancing age, but I think it unwise for most sociological aspirants to invest the time and effort needed to master the theory of directed graphs.The promise that at first seemed so obvious just isn't there.On the other hand, if you just like math, this is a good book.If you really have a flair for this sort of thing, a career in the prestigious, even if sterile, sub-discipline of mathematical sociology may be in your future. ... Read more

Product Description
First published in 1976, this book has been widely acclaimed as a major and enlivening contribution to the history of mathematics. The updated and corrected paperback contains extracts from the original writings of mathematicians who contributed to the foundations of graph theory. The author's commentary links each piece historically and frames the whole with explanations of the relevant mathematical terminology and notation. ... Read more

Customer Reviews (1)

Some interesting episodes from the history of graph theory
This book teaches basic graph theory through excerpts from original papers in English translation. In between, the authors discuss the history and the mathematical concepts at an elementary level, hoping that the book may serve as a first textbook of graph theory. I think it could serve this purpose very well. There is a lot of focus on the puzzle-style origins of graph theory, starting with marvelous 18th century classics of Euler and Vandermonde and then including many other charming little topics like for instance a very nice 1895 paper of Tarry on how to find your way out of a maze. There are also topics from other fields (e.g. chemistry), but here I think the background discussions are a bit weak. Something like half the book is centred around the four-colour problem, which is historically faithful and necessary, but it is obviously disturbing that the book ends long before this problem was solved. ... Read more

Product Description
In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson's book has been widely used as a text for undergraduate courses in mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians.The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their efficiency. ... Read more

Customer Reviews (4)

Charming introduction
This author has a charming writing style, although he suffers from a mathematician's sense of humor.A light introduction to graph theory, suitable for a beginning undergraduate student.Nothing is covered particularly in-depth, and the more difficult proofs are passed over and left to the reader to find and master.The exercises are very important--many of the most important theorems are hidden in there.This text is suitable for independent study, although an advisor would be helpful simply because the theorems hidden in the exercises make you want to have your homework checked.
A further note on proofs: many of those that the author does include are constructionist, and seem to involve a lot of hand-waving.There are very few rigorous proofs, and a teacher using this book should instruct his or her students in the more formal approach to graph theory proofs.This text could benefit from including more.

On the whole: nice diagrams, good notation, good order of material, and very accessible.

I read this text during an undergraduate combinatorics course after having taken a semester of introductory graph theory.

Not at this price
This is a very, very thin introductory work on graph theory.

It loses one star because the section numbering and the chapter numbering aren't aligned correctly. (The section numbers increase monotonically from 1 to N. Chapter breaks are inserted almost randomly as a way of grouping sections.)

It loses another star because it doesn't serve the needs of beginners very well. As a previous reviewer has pointed out, it doesn't contain many examples, and results are often stated with only sketch proofs.

It loses one final star because of its ridiculous price. For the same dollar amount, one could buy a good introductory book (such as Chartrand's "Introduction to Graph Theory"), a Schaum's outline (for solved problems), and a decent high-level book for mathematical depth.

On the positive side, Prentice did print this thing on good paper...

The worst book in graph theory
I have found this book difficult to read because of its lack of examples and theorems.Many famous examples and theorems are left as exercises.Many of them are too difficult for a beginner.The book just state some basic defintion and theorem without examples, and even some proofs of the theorems are not complete.Many algorithms are skipped or illustrated badly.I can give no reason for the beginner to buy this book. I would suggest the reader to see "A first Look At Graph Theory" by John O. Clark

Great introductory text!!
A great -and gentle - introduction to Graph Theory...clear definitions and examples, great figures,useful exercises, and even some cleverquotes.Everything you could ask for - if only all texts were this clearand well-organized.This was my first foray into the topic, and Wilson'stext made it enjoyable. ... Read more

Product Description

This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.