Opis: The Fascinating World of Graph Theory - Ping Zhang, Gary Chartrand, Arthur Benjamin

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 Konigsberg 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. "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 blogPreface 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

Szczegóły: The Fascinating World of Graph Theory - Ping Zhang, Gary Chartrand, Arthur Benjamin

Tytuł: The Fascinating World of Graph Theory
Autor: Ping Zhang, Gary Chartrand, Arthur Benjamin
Producent: Princeton University Press
ISBN: 9780691163819
Rok produkcji: 2015
Ilość stron: 344
Oprawa: Twarda
Waga: 0.71 kg

Recenzje: The Fascinating World of Graph Theory - Ping Zhang, Gary Chartrand, Arthur Benjamin