Graph Theory: An Introduction to Proofs, Algorithms, and Applications (Paperback)
暫譯: 圖論：證明、演算法與應用入門（平裝本）

Karin R Saoub

Graph Theory: An Introduction to Proofs, Algorithms, and Applications (Paperback)
  • 出版商: CRC
  • 出版日期: 2021-03-17
  • 售價: $1,350
  • 貴賓價: 9.8 折 $1,323
  • 語言: 英文
  • 頁數: 421
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 0367743752
  • ISBN-13: 9780367743758
  • 相關分類: Algorithms-data-structures

    • 立即出貨 (庫存=1)

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相關主題

商品描述

Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis.

 

This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results.

Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations.

 

Current applications and exploratory exercises are provided to further the reader's mathematical reasoning and understanding of the relevance of graph theory to the modern world.

 

Features

　

 

 

 

 

 

 

 

 

 

 

  • The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book
  • The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths.
  • The third chapter focuses entirely on trees - terminology, applications, and theory.
  • Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach.
  • Hints and Solutions to selected exercises provided at the back of the book.

 

商品描述(中文翻譯)

圖論是研究互動、衝突和連結的學科。離散物件集合之間的關係可以告訴我們它們所處的整體網絡，而圖論可以提供分析的途徑。

本書是針對第一門本科課程，將從理論和應用的角度探討圖論的主要主題。主題將從理解基本術語開始，接著解決計算問題，最後以廣泛的理論結果作結。

範例和練習將引導讀者逐步進入這一過程，特別注意加強證明技巧和書面數學解釋。

本書提供當前應用和探索性練習，以進一步提升讀者的數學推理能力，並理解圖論在現代世界中的相關性。

**特色**

- 第一章介紹圖的術語、使用圖的數學建模，以及本書中出現的證明技巧回顧。
- 第二章探討三個主要路徑問題：歐拉迴路（eulerian circuits）、哈密頓迴圈（hamiltonian cycles）和最短路徑（shortest paths）。
- 第三章專注於樹的相關內容，包括術語、應用和理論。
- 另外四章圍繞一個主要的圖概念：連通性（connectivity）、匹配（matching）、著色（coloring）和平面性（planarity）。每一章都引入一個現代應用或方法。
- 書末提供選定練習的提示和解答。

作者簡介

 

Dr. Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She received her PhD in Mathematics from Arizona State University and a Bachelor of Arts degree from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.

作者簡介(中文翻譯)

卡琳·R·薩烏布博士是維吉尼亞州薩勒姆的羅阿諾克學院數學副教授。她在亞利桑那州立大學獲得數學博士學位，並在威爾斯利學院獲得文學士學位。她的研究專注於圖著色和應用於容忍圖的線上算法。她也是由CRC Press出版的《圖論之旅》（A Tour Through Graph Theory）的作者。

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