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.
Autorentext
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.
Zusammenfassung
The history, formulas, and most famous puzzles of graph theoryGraph 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.
Inhalt
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