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The Fascinating World of Graph Theory

Summary

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.

Authors

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.

References

The Fascinating World of Graph Theory, Arthur Benjamin, Gary Chartrand, Ping Zhang, Princeton University Press, 2015.


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