Graph Theory: An Introduction to Proofs, Algorithms, and Applications (Paperback)
Karin R Saoub
- 出版商: CRC
- 出版日期: 2021-03-17
- 定價: $1,350
- 售價: 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
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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、衝突和連接的學科。離散物件之間的關係可以告訴我們它們所在的整體網絡,而圖論可以提供一種分析的途徑。
這本教材是為第一個本科課程而設計的,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,解決計算問題,最後以廣泛的理論結果結束。
例子和練習將引導讀者進行這個過程,特別關注加強證明技巧和書面數學解釋。
提供當前應用和探索性練習,以進一步培養讀者的數學推理能力,並理解圖論對現代世界的相關性。
特點:
- 第一章介紹圖的術語,使用圖進行數學建模,並回顧全書中使用的證明技巧。
- 第二章研究三個主要的路徑問題:歐拉迴路、漢米爾頓環和最短路徑。
- 第三章完全聚焦於樹-術語、應用和理論。
- 四個額外的章節圍繞著一個主要的圖概念:連通性、匹配、著色和平面性。每個章節都引入了一個現代應用或方法。
- 提供選定練習的提示和解答。
(此為書籍翻譯助手提供的翻譯,僅供參考)
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)
Dr. Karin R. Saoub 是維吉尼亞州Salem的羅諾克學院的數學副教授。她在亞利桑那州立大學獲得數學博士學位,並在韋爾斯利學院獲得文學學士學位。她的研究專注於圖著色和應用於容忍圖的在線算法。她還是CRC Press出版的《圖論之旅》的作者。