图论教程

所属分类:数学  
出版时间:2011-6   出版时间:科学出版社   作者:(印)巴拉克里什南 等编著   页数:227  
Tag标签:图论,数学,英语  

内容概要

Graph theory has experienced a
tremendous growth during the 20thcentury. One of the main reasons
for this phenomenon is theapplicability of graph theory in other
disciplines such as physics,chemistry, psychology, sociology, and
theoretical computer science.This book aims to provide a solid
background in the basic topics ofgraph theory. It covers Dirac's
theorem on k-connected graphs,Harary-Nashwilliam's theorem on the
hamiltonicity of line graphs,Toida-McKee's characterization of
Eulerian graphs, the Tutte matrixof a graph, Foumier's proof of
Kuratowski's theorem on planar graphs,the proof of the
nonhamiltonicity of the Tutte graph on 46 verticesand a concrete
application of triangulated graphs. The book does notpresuppose
deep knowledge of any'branch of mathematics, butrequires only the
basics of mathematics. It can be used in an advancedundergraduate
course ora beginning graduate course in graph theory.

作者简介

作者:(印度)巴拉克里什南(R.Balakrishnan) (印度)K.Ranganathan

书籍目录

Preface
Ⅰ Basic Results
1.0 Introduction
1.1 Basic Concepts
t.2 Subgraphs
1.3 Degrees of Vertices
1.4 Paths and Connectedness
1.5 Automorphism of a Simple Graph
1.6 Line Graphs
1.7 Operations on Graphs
1.8 An Application to Chemistry
1.9 Miscellaneous Exercises
Notes
Ⅱ Directed Graphs
2.0 Introduction
2.1 Basic Concepts
2.2 Tournaments
2.3 k-Partite Tournaments
Notes
Ⅲ Connectivity
3.0 Introduction
3.1 Vertex Cuts and Edge Cuts
3.2 Connectivity and Edge-Connectivity
3.3 Blocks
3.4 Cyclical Edge-Connectivity of a Graph
3.5 Menger's Theorem
3.6 Exercises
Notes
Ⅳ Trees
4.0 Introduction
4.1 Definition, Characterization, and Simple Properties
4.2 Centers and Centroids
4.3 Counting the Number of Spanning Trees
4.4 Cayley's Formula
4.5 Helly Property
4.6 Exercises
Notes
Ⅴ Independent Sets and Matehings
5.0 Introduction
5.1 Vertex Independent Sets and Vertex Coverings
5.2 Edge-Independent Sets
5.3 Matchings and Factors
5.4 Matchings in Bipartite Graphs
5.5* Perfect Matchings and the Tutte Matrix
Notes
Ⅵ Eulerian and Hamiltonian Graphs
6.0 Introduction
6.1 Eulerian Graphs
6.2 Hamiltonian Graphs
6.3* Pancyclic Graphs
6.4 Hamilton Cycles in Line Graphs
6.5 2-Factorable Graphs
6.6 Exercises
Notes
Ⅶ Graph Colorings
7.0 Introduction
7.1 Vertex Colorings
7.2 Critical Graphs
7.3 Triangle-Free Graphs
7.4 Edge Colorings of Graphs
7.5 Snarks
7.6 Kirkman's Schoolgirls Problem
7.7 Chromatic Polynomials
Notes
Ⅷ Planarity
8.0 Introduction
8.1 Planar and Nonplanar Graphs
8.2 Euler Formula and Its Consequences
8.3 Ks and K3.3 are Nonplanar Graphs
8.4 Dual of a Plane Graph
8.5 The Four-Color Theorem and the Heawood Five-Color Theorem
8.6 Kuratowski's Theorem
8.7 Hamiltonian Plane Graphs
8.8 Tait Coloring
Notes
Ⅸ Triangulated Graphs
9.0 Introduction
9.1 Perfect Graphs
9.2 Triangulated Graphs
9.3 Interval Graphs
9.4 Bipartite Graph B(G) of a Graph G
9.5 Circular Arc Graphs
9.6 Exercises
9.7 Phasing of Traffic Lights at a Road Junction
Notes
Ⅹ Applications
10.0 Introduction
10.1 The Connector Problem
10.2 Kruskal's Algorithm
10.3 Prim's Algorithm
10.4 Shortest-Path Problems
10.5 Timetable Problem
10.6 Application to Social Psychology
10.7 Exercises
Notes
List of Symbols
References
Index

章节摘录

版权页:插图:

图书封面

图书标签Tags

图论,数学,英语


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用户评论 (总计21条)

 
 

  •     内容很具体,有形象的解释和图~便于学习,很新喔,惹人爱喔
  •     不知道!,是我想要的那本书
  •     讲的挺细的,但是运送时间太长了。
  •     很厚。,前言写成言前了
  •     还是很不错的一本书,没有练习题
  •     还在看,希望不要太难了
  •     还行吧,中科大的教材都不错啊
  •     感觉不错呦!下次还来~,发货挺快
  •     讲得比较详细,不过送来的时候纸张被折烂了。
  •     内容详细充实准确,算法的基础是离散数学
  •     就會有圖論基本概念。,讲的很有条理
  •     先攒本书看看,英文原版
  •     值得大家去学习;赞 一个,书很快回来了
  •     图论的相关内容,值得一看!推荐
  •     送货速度快,期待很久的书一本
  •     质量好!,国内教材中的精品
  •     简单朴实,不过软件应用方面介绍相对较少
  •     值得学习参考!,東西不錯…但快遞沒有按註明的時間段投送
  •     不过内容十分全面!,很不错的一本书
  •     研究生准备自学这个方面,写的过于简单
  •     本书作者是国家奥数权威,是英文版的教材呀
 

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