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Provides a solid background in the basic topics of graph theory.Does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. DLC: Graph theory. ... 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

Product Description
This text offers an introduction to the theory of graphs and its application in engineering and science. The first part covers the main graph theoretic topics: connectivity, trees, traversability, planarity, coloring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. In the second part, these concepts are applied to problems in engineering, operations reserach, and science as well as to an interesting set of miscellaneous problems, thus iluustrating their broad applicability. Some effort has been made to present applications that use not merely the notation and terminology of graph theory, but its actual mathematical results. Some of the applications, such as in molecular evolution, facilities layout, and graffic network design, have never appeared before in book form. Written at an advanced undergraduate to beginning graduate level, the book is suitable for students of mathematics, engineering, operations resrach, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling. ... Read more

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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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Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, such as approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms. ... Read more

Customer Reviews (3)

literate programming killed the book
Good on describing graph theory algorithms but is rendered bad due to that literate programming ... Simple algorithmic notation would have made the book much better...

Book centered entirely on combinatorial subgraph problems
This book's title is very misleading, as the author's focus really is on subgraph problems (e.g. subgraph and tree isomorphism, clique, independent set, and vertex cover).

The book barely mentions other graph theory topics such as distance algorithms (e.g. single-source shortest path, minimum-spanning tree, transitive closure), network flow, or graph colouring. This odd focus is really frustrating since the author spends a large number of pages on relatively simple topics such as tree traversal (34 pages on things like pre-order traversal) and graph traversal (42 pages on things like depth-first search). In fact, in section 5.3 on graph traversal applications, the author suggests that the reader may have already learned about algorithms such as shortest path or topological sorting, so he instead gives an example of ordered graph isomorphism. I do not understand why the author would make such an assumption; if the reader is assumed to already know about many applications of graph traversal, then why did the author spend 42 pages explaining what graph traversal is?

I believe one possible reason why the author does not discuss such "simpler" graph algorithms is that the LEDA library already has functions that implement algorithms like Dijkstra's, Bellman-Ford, MST, and max flow. However, the author does not spend time even defining what these problems are and only mentions the existence of these functions in the appendix.

Other things I did not like about the book:

- Much of the material seems to be simply cut-and-paste from one topic to the next. Case in point: the chunk of text saying "The problem of [problem] belongs to the class of NP-complete problems ... size of the graph" is pasted verbatim into at least four sections. Other lengthy passages are similarly pasted.

- The author's writing style makes reading the book more of a chore than it needs to be. My philosophy is that simple ideas should be explained simply, and I posit that this philosophy should be applicable to a depth-first traversal of a graph. However, the author is a bit formal in his explanation of DFS (among other topics), saying that "a simple procedure for a depth-first traversal of a graph consists of performing a preorder traversal upon each of the depth-first trees in the depth-first spanning forest of the graph" (p. 261). Compare this definition to the more fluid and intuitive definitions given by CLRS (2001) on page 540 and by Sedgewick's (Graph) Algorithms in C++ (2002) on page 87.

- As a minor point, the author uses the term "arc" whereas in the literature the more common term is "edge". I suppose this is not a big deal, but then the author defines a graph as having a vertex set V and an arc set E. Furthermore, in the LEDA appendix where the author is discussing the graph API that has word "edge" in the function calls (e.g. number_of_edges()), the author continues to use the term "arc".

- I am not sure if the C++ implementions using LEDA provided by the author really are helpful enough to outweigh their terseness and difficulty for reading. A better approach might have been CLRS-style pseudocode to explain the implementations. However, this book is really more of a LEDA applications guide, and I believe many people will find the code examples to be very helpful.

Now, here are the good points of this book that raise my rating from 3 stars to 4:

+ Chapter 2 is very, very nice. It uses a recurring example problem of tree edit-distance throughout four sections on backtracking, branch-and-bound, divide-and-conquer, and dynamic programming, thereby allowing the user to see how these different algorithmic approaches differ for a fixed problem. The discussion on tree edit-distance itself was new to me and very interesting.

+ The author makes nice use of examples throughout the book. Almost every theorem and definition is accompanied by an illustrated example.

+ The references are very thorough (at least for the time that the book was published), and the bibliographic section in each chapter, while short, frame the related work references very well.

+ The author consistently uses backtracking throughout the subgraph algorithm implementations, so it was good to hammer that down for the reader. However, it would have been nice to see the author discuss different implementations using dynamic programming (to attain some pseudo-polynomial time algorithm perhaps), approximation algorithms, or stochastic search (e.g. genetic algorithms).

In summary, this is a good book, but only if you are interested in the subgraph problems that the author covers.

Intersting Studies Hampered by LEDA and LP Dependencies
I'm pleased with the text in this book; the descriptions are almost all clear, and reading through the book gives me insight into some more interesting problems in trees and graphs. The high points of the book are its treaments of tree and graph isomorphism, but I also found the discussions of non-traditional traversal algorithms on trees and graphs very interesting. The author discussions leaf-first, breadth-first, and depth-first traversals and provides algorithms for their implementation. Many of the algorithms include correctness proofs.

These topics alone made the book worth its to me. A deep academic book that costs less than $50 is nearly unheared-of.

Unfortunately, there are two flaws that make the book hard to use. In a nutshell, the author expects the reader to buy into a couple of pretty invasive and expensive propositions.

First, the author decided to use literate programming for all of his presented algorithms and code fragments. This isn't so bad, since literate programming is about documenting code. If you suppose that the author wrote the code, then documented it, then calld it a book, using a tool like literate programming seems like a natural choice.

But if you're not familiar with literate programming, it's a bit of a chore. The author's introduction to literate programming doesn't help with some of the questions even an experienced programmer might have wend reading the text. More practically, literate programming enforces operators that are different than most C/C++ developers are familiar with, and can cause confusion when reading the text. ^ is used, for example, to indicate a logical and, where C/C++ developers expect it to indicate a bitwise-exclusive or.

While it's esay to eventually overcome such tricks of memory, I've been finding it hard to scan literate programs to find definitions and declarations. The author doesn't include a CD (and at this cover price, that is hard to fault) but also doesn't make his code available for download. His website includes a LEDA-based program that interactively demonstrates some algorithms, but doesn't include code for the algorithm his own books develops and discusses.

The other decision made by the author, to the overwhelming inconvenience of this reader, is the reliance on the LEDA library for his samples and programs. The algorithms are understandable without the library, but a reader without access to LEDA doesn't benefit from any of the visualizations the author provides. , and several include

In fact, the author spends about 40 pages discussing LEDA and the characteristics of its implementation. Maybe researchers working on tree and graph algorithms all use LEDA and have ready access to it, but the literate programming code provided to for some of the algorithms isn't useful to readers who aren't familiar with LEDA, as researching the definitions and declarations themsleves becomes arduous.

The bibliography is very diverse, with more than 380 entries and is well-cited throughout the book. Unfortunately, the author sometimes relies on the bibliography too much. On page 392, the author brings up "the so-called graph isopomorphism disease" without defining it himself; he instead relies on his bibliography entries to give the user any definition or background on the "disease".

Unfortunately, the index received not nearly as much attention as the bibliography; neglecting whitespace, it's scarcely more than a single page long!

The book appears to be something more than a research paper, but is written much like a research apper would be. The book probably also serves well for a class that teaches this subject, and assumes LEDA and literate programming as prerequisites. But as a commercial developer who's interested in applying advanced graph and tree algorithms to the work I'm doing, I found the book has limited its value by relying on LEDA and applying literate programming.

All this said, I still feel it's appropriate to give the book four stars. The material covered is hard to find elsewhere, and with some effort I can overcome the LEDA and literate programming hurdles. Since I don't use LEDA or literate programming day-to-day, I'll have to overcome that unfamiliarity every time I pick up the book as a reference. ... 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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In this substantial revision of a much-quoted monograph first published in 1974, Dr. Biggs aims to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first section, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject that has strong links with the "interaction models" studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory.The structure of the volume is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of "Additional Results" are included at the end of each chapter, thereby covering most of the major advances in the past twenty years.This new and enlarged edition will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists. ... Read more

Customer Reviews (2)

Clear and (mostly) to the point
This is a very nice book, which gives an introduction to some active areas of current research, but it does not really have too much depth (even in the references), so if you are doing research in this or related subjects, I would recommendSpectra of Graphs, 87: Theory and Application (Pure and Applied Mathematics (Academic Pr)) (yes, it is out of print, and yes, it costs a mint, but your university library probably has it). Godsil's book (referered to in a previous review) is much more algebraic and much less pleasant to read than Biggs.

Well written, intriguing, but somewhat dated
I found this book very clear, concise, and well written. Most proofs seemed effortless on both the author's and reader's part. Moreover, I found the content very interesting, especially the results on the spectrum of a graph, which simply represents the eigenvalues (and their multiplicities) of the adjacency matrix (although recently it has been defined in terms of the normalized incidence matrix). It amazed me just how much mathematics can be put to bear on such a simple notion of vertices and connections between them. The only downside to this book is that algebraic graph theory has moved in many new directions since the first edition (the second edition mostly states some recent results at the end of each chapter), and the interested reader may want to supplement this book or follow up this book with the following: "Spectral Graph Theory", by Fan Chung, "Algebraic Graph Theory", by Godsil et al., and "Modern Graph Theory", by Bollobas, all of which make for graduate-level reading. And to think that some mathematics departments still show little if any desire to support fellow mathematicians who study graph theory! Reading any of these books hopefully might alter some of those entrenched attitudes. ... 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
The book is intended to be an introductory text formathematics and computer science students at the second and third yearlevel in universities. It gives an introduction to the subject withsufficient theory for that level of student, with emphasis onalgorithms and applications. ... Read more

Customer Reviews (3)

Answer key?
I am working on this book on my own. There are a number of errors, even in the first chapter. I'm surprised, given that the book has had five reprintings! Is there an errata sheet available? How about an answer key? These errors make the book difficult to work with without a teacher.

A suitable text for an undergraduate course
This book seems to be one of the best choices of the text for an undergraduate course. It covers all topics that can be included in such course. It contains many exercises. Some of the exercises are routine, some others are more challenging. Also the price of the paperback edition is quite reasonable for a text for a semester course.
I should mention that there are some misprints in this text. Also, there are some gaps in the proof of the Brooks' theorem (pp. 194-196). So a new corrected printing is desirable.

A First Look at Graph Theory
Deseo este libr ... 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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Substantially revised, reorganised and updated, the second edition now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems.

As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem.

Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject.

Customer Reviews (2)

Good for experts and researchers but not for beginners
I come across this book when finding relevant materials of graph theory.As told by previous reviewer, this book contains much recent research results and is good for experts or researchers.The preface says that it is suitable for undergraduate, but in my feeling, you need to be a graduate with a full year course of graph theory completed to understand or utilize the materials of the book.The materials are presented in a standard theorem-proof format, one theorem after another.Examples are few.Though the book title contains "Algorithm", there are also few algorithms presented in the form you saw in books of computing. Probably you need to design your own algorithm after digesting the material.Besides, exercises are abundant but no hints or answers provided.

Directed graphs are more general than undirected graphs
This book reflects the main achievements of the last three decades in the directed graphs theory as well as many applications including combinatorial optimization, operations research and the fascinating area of mathematics and computer science called discrete mathematics. Since the monograph contents are given, I do not wish to go into details of material presented there.Instead I'd like to discuss the aims of the book as well as whocould be its readers.

The text strives to accomplish the following objectives:

1. To give a great deal of information on both results and prooftechniques for specialists in graph theory.No other book covers even 10\% of material provided in Digraphs,and thus before this monograph has beenpublished even specialists in graph theory very often needed tosearch for a specific result or proof techniquethrough the ocean of literature on digraphs. Now the situation has drastically improved.

2. To introduce researchers and practitioners from various otherfields in mathematics, computer science,operations research, biology, etc. to basic and more advancedresults in digraph theory and algorithms andsome carefully selected applications. It offers much more thanmerely a pure bibliography and provides theideal starting point for any researcher who needs to becomefamiliar either with theory oriented aspects ofthis interesting area or with some application in a relatively short time.

3. To provide enough material for intermediate and final year BSc or MSc courses for students in mathematics, computer science and operations research. The large number of exercises (more than 700) of various difficulty is of great help to instructors and lecturers. The applications provided in the book will help to provide enough motivation for the students to study digraph theory and algorithms.

4. To provide a large variety of topics for final year student projects in mathematics, computer science, operations research and other fields. The monograph can be used as a source for the projects because because several areas of digraph theory are covered there in real depth and they vary from relatively simple to reasonably complicated ones.

To summarize, I'd like to notice that the monograph is aimed to awide range of readers including specialists in mathematics, operations research, computer science, biology, etc.as well as students of second year and higher.

Boris Goldengorin, Department of Econometricsand Operations Research, University of Groningen, The Netherlands ... Read more

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A comprehensive look at the emerging science of networks

Network science helps you design faster, more resilient communication networks; revise infrastructure systems such as electrical power grids, telecommunications networks, and airline routes; model market dynamics; understand synchronization in biological systems; and analyze social interactions among people.

This is the first book to take a comprehensive look at this emerging science. It examines the various kinds of networks (regular, random, small-world, influence, scale-free, and social) and applies network processes and behaviors to emergence, epidemics, synchrony, and risk. The book's uniqueness lies in its integration of concepts across computer science, biology, physics, social network analysis, economics, and marketing.

The book is divided into easy-to-understand topical chapters and the presentation is augmented with clear illustrations, problems and answers, examples, applications, tutorials, and a discussion of related Java software. Chapters cover:

• Origins

• Graphs

• Regular Networks

• Random Networks

• Small-World Networks

• Scale-Free Networks

• Emergence

• Epidemics

• Synchrony

• Influence Networks

• Vulnerability

• Net Gain

• Biology

This book offers a new understanding and interpretation of the field of network science. It is an indispensable resource for researchers, professionals, and technicians in engineering, computing, and biology. It also serves as a valuable textbook for advanced undergraduate and graduate courses in related fields of study. ... Read more

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This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

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Customer Reviews (1)

The classic text on the subject
After a long period of being out of print, Welsh's classic text is now available again in a very affordable Dover edition.This is great news, not only for specialists in matroid theory but also for researchers in graph theory, combinatorial optimization, and combinatorial differentiable geometry, all of which use matroids.

Those contemplating buying this book may want to know how it differs from other texts on the subject.The closest book is Oxley's.Oxley himself explains the difference in his introduction: "[Welsh's book] appeared during my second year at Oxford and it has been my constant companion ever since.When I contemplated writing this book, the first question I had to answer was how should it differ from Welsh's book.This book attempts to blend Welsh's very graph-theoretic approach to matroids with the geometric approach of Rota's school that I learnt from Brylawski.Unfortunately, I cannot emulate Welsh's feat of providing, in a single volume, a complete survey of the current state of knowledge in matroid theory; the subject has grown too much.Therefore I have had to be selective.While the basic topics virtually select themselves, the more advanced topics covered here reflect my own research interests."

While there is some overlap between the two books, Welsh's book contains a lot of material not available elsewhere.Two examples that come to mind immediately (because I had reason to look them up recently) are the topics of base-orderability and of strong and weak maps, but there are many others.Welsh's book is indispensable and it is a credit to Dover Press that they recognize its continuing value to this active area of current mathematical research. ... Read more

Product Description

Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem.

Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.

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The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

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This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications.The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions.The final part of the book presents the tools of "modern" set theory: Martin's Axiom, the Diamond Principle, and elements of forcing.Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields. ... Read more