The Fascinating World of Graph Theory (Hardcover)

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.

迷人的圖論世界可以追溯到數個世紀前，圍繞著研究圖形的數學結構，展示了物體之間的關係。圖論在生物學、計算機科學、交通科學和其他領域中應用廣泛，涵蓋了數學中最美麗的公式之一，以及其中一些最著名的問題。例如，對於一個旅行業務員在一次旅行中訪問多個城市，最短路徑是什麼？在填色地圖時，需要最少的顏色數量，以便相鄰區域始終以不同的顏色填充？本書要求讀者具備高中代數的數學背景，探索了通過圖論研究並且通常已經解決的問題和謎題。在此過程中，本書探討了圖論的發展以及推動該領域增長的活躍人士。

作者介紹了圖論的基本概念，並探討了各種經典問題，如熄燈謎題、最小生成樹問題、肯尼斯堡橋問題、中國郵差問題、騎士之旅和道路著色問題。他們介紹了各種可能的圖形，如二分圖、歐拉圖、彼得森圖和樹。每章都包含數學練習和問題，供讀者品味。

這本書帶領讀者進入圖論的世界，提供了令人興奮的數學解決問題的可能性，不僅僅限於數學領域。