Benjamin A. The Fascinating World of Graph Theory 2015 torrent

Textbook in PDF format

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.
Prologue.
Introducing Graphs.
Classifying Graphs.
Analyzing Distance.
Constructing Trees.
Traversing Graphs.
Encircling Graphs.
Factoring Graphs.
Decomposing Graphs.
Orienting Graphs.
Drawing Graphs.
Coloring Graphs.
Synchronizing Graphs.
Epilogue. Graph Theory: A Look Back — The Road Ahead.
Exercises.
Selected References.
Index of Names.
Index of Mathematical Terms