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
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
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 is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms. A number of exercises and outlines of solutions are included to extend and motivate the material of the text. ... Read more

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This outstanding new book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory. ... 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
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
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
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

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The popular Rookie Books expand their horizons - to all corners of the globe! With this series all about geography, emergent readers will take off on adventures to cities, nations, waterways, and habitats around the world…and right in their own backyards. ... Read more

Customer Reviews (1)

Graphical Mathical Fun
This is an exciting first look at the utility and function of graphs, set within a "field trip to the zoo" narrative. Author Melissa Stewart has written more than 60 books for kids and frequently contributes to publisher Scholastic's MATH magazine, and Dr. Cecilia Minden_Cup of Harvard served as the readability consultant.

The zoo is an ideal setting for applied math: There arre animals to count and sizes to compare. The photographs (from the San Frnacisco zoo) are breezy and uncluttered, although otherwise unremarkable.However, they do add some flavor to the two main math techniques presented:Tallying, as in ||||= 4, and bar graphs, which are especially useful when comparing height:The taller the bar, the taller the "animal's shoulder height (the height without measuring the neck and head)." This presentation is intuitive and fun, and leads to slightly more abstract concepts.A "taller" bar can also mean that there is more of something--it doesn't necessarily mean how tall something is.

The book argues persuasively for hte importance of learning graphs and pther forms of pictorial representations: "My teacher says that a picture is worth a thousand words."Three pages later, after showing a boy/girl/total students bar graph, this cliche is followed by a more surprising observation for the young reader: "MY teacher also says that a graph is worth a thousand bumbers." 32 shiny pages, with an overview of words and concepts, as well as a brief index, this is an excellent, non-threatening introduction to graph power! ... Read more

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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
Designed for the nonspecialist, this classic text by a world expert is an invaluable reference tool for those interested in a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding as both a text and reference for students and researchers in graph theory and its applications. The reader will delight to discover that the topics in this book are coherently unified and include some of the deepest and most beautiful developments in graph theory. ... Read more

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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

Customer Reviews (2)

Clear, a pleasure to read for a beginner
The writing is excellent. I got an introduction to graph theory from Mark Allen Weiss' "Data structures and algorithm analysis in C++". That was a very good start and led me to think I could use graph theory to solve a problem. When I needed to probe deeper I found this book in Weiss' bibliography. I read the first few chapters and felt comfortable enough to go out on the internet and find a PhD thesis that applied directly to my problem.

Clearly built up, and straightforward
I was using this book as the first book for a Graph theory course and have choosen thisfrom about 10 (pre-selected) books. It is interesting as it opens up new areas by solving interesting problems. I am not a professionalin Graph Theory as i am doingComputer Science but i haven't found betterintroductory book so far. ... Read more

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Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices.

After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry.

Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas. ... Read more

Product Description
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the subject. An appendix outlines the basis of computational complexity theory, in particular the definition of NP-completeness, which is essential for algorithmic applications. ... Read more

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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

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