The Fascinating World of Graph Theory

by Arthur Benjamin, Gary Chartrand, Ping Zhang

Overview

The history, formulas, and most famous puzzles of graph theory

Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

Product Details

ISBN-13:	9780691175638
Publisher:	Princeton University Press
Publication date:	06/06/2017
Edition description:	Reprint
Pages:	344
Sales rank:	1,163,310
Product dimensions:	6.10(w) x 9.20(h) x 1.00(d)

About the Author

Arthur Benjamin is professor of mathematics at Harvey Mudd College. Gary Chartrand is professor emeritus of mathematics at Western Michigan University. Ping Zhang is professor of mathematics at Western Michigan University.

Table of Contents

Preface vii

Prologue xiii

1 Introducing Graphs 1

2 Classifying Graphs 22

3 Analyzing Distance 45

4 Constructing Trees 67

5 Traversing Graphs 91

6 Encircling Graphs 108

7 Factoring Graphs 125

8 Decomposing Graphs 143

9 Orienting Graphs 164

10 Drawing Graphs 183

11 Coloring Graphs 206

12 Synchronizing Graphs 226

Epilogue Graph Theory: A Look Back—The Road Ahead 251

Exercises 255

Selected References 309

Index of Names 317

Index of Mathematical Terms 319

What People are Saying About This

From the Publisher

"In this attractive introduction to the world of graphs, the authors entice and enthuse readers through a number of fun problems which present various aspects of the subject. Many of these problems are familiar—the four-color problem, the Königsberg Bridge problem, and 'instant insanity'—while others are less well known or of a more serious nature. This book can be used in different ways—as an entertaining book on recreational mathematics or as an accessible textbook on graph theory. I warmly recommend it."—Robin J. Wilson, author of Introduction to Graph Theory

"This is a beautiful introduction to graph theory! It is filled with fun material, clear explanations, and a nice collection of exercises. A great book."—William J. Cook, author of In Pursuit of the Traveling Salesman

"The Fascinating World of Graph Theory is wonderfully written. Entertaining applications appear first and the stories that accompany the examples go well beyond what most other books provide. This book is sure to gain a following."—Jonathan L. Gross, Columbia University

Editorial Reviews

One of Choice's Outstanding Academic Titles for 2015

From the Publisher

"[The authors] have set out to make graph theory not only accessible to people with a limited mathematics background, but also to make it interesting. They have—by virtue of very clear writing, combined with a greater-than-usual emphasis on the historical and personal side of the subject—succeeded admirably."

MAA Reviews

"A fun and interesting tour of graph theory, leaving each visitor with a feeling of accomplishment and a satisfying understanding of this unusual mathematical world. . . . This is an entertaining book for those who enjoy solving problems, plus readers will learn about some powerful mathematical ideas along the way!"

Choice

"Deftly written and dynamic. . . .The Fascinating World of Graph Theoryis an aptly named book, able to present a wide variety of central topics in graph theory, including the history behind them. . . in a lively and entertaining manner. . . . A superb example of approachable mathematical writing."

SIAM Review

"The Fascinating World of Graph Theory shows its pedagogic value. Traditional courseware develops subject matter from the bottom on up, going from basic definitions to the more complex. [This book] is different, not starting with the simplest structures or algorithms but with interesting problems to be solved, puzzles that use graphs and networks. . . . [It is] readable and ‘student-friendly'—more so than the typical math textbook."

New York Journal of Books