The fascinating world of 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. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory’s development and the vibrant individuals responsible for the field’s growth.
Introducing graph theory’s fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Königsberg Bridge Problem, the Chinese Postman Problem, a Knight’s Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor.
An eye-opening journey into the world of graphs, this book offers exciting problem-solving possibilities for mathematics and beyond.
Arthur Benjamin is professor of mathematics at Harvey Mudd College. His books include Secrets of Mental Math and Proofs That Really Count. Gary Chartrand is professor emeritus of mathematics at Western Michigan University. Ping Zhang is professor of mathematics at Western Michigan University. Chartrand and Zhang are the coauthors of several books, including A First Course in Graph Theory and Discrete Mathematics.
"The Fascinating World of Graph Theory is readable and 'student-friendly'--more so than the typical math textbook."--Robert Schaefer, New York Journal of Books
"[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."--Mark Hunacek, MAA Reviews
"The book is written masterfully; the narrative in each chapter flows naturally, engagingly. . . . [I]t's a popular but also comprehensive introduction into graph theory."--Alexander Bogomolny, Cut the Knot blog
"This book is 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
"Here is a book with an enjoyable mix of mathematics and its applications, spiced with liberal amounts of history and anecdote. . . . The value of books like this is that they make mathematics come alive to a broad range of readers who might not look twice at a textbook or monograph."--Norman Biggs, London Mathematical Society Newsletter
Table of Contents:
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
Selected References 309
Index of Names 317
Index of Mathematical Terms 319