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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. One of Choice's Outstanding Academic Titles for 2015 "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 "[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 "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 "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 "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 authors manage to motivate all topics with interesting applications, historical problems and discussion of concepts from an intuitive point of view."--Radu Trimbitas, Studia Mathematica "I am not going to try to list the topics that are covered, since there is a great variety. This breadth, along with the superb writing, make the book a must-have for anyone with serious interest in graph theory."--James M. Cargal, UMAP Journal

The Fascinating World of Graph Theory

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