图书信息

内容简介

作者简介

图书目录

图书信息

书 名: 图论教程

作　者：巴拉克里什南

出版社： 科学出版社

出版时间： 2011年6月1日

ISBN: 9787030313850

开本： 16开

定价: 66.00元

内容简介

这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些书也具有交叉性质。这些书都是很新的，2000年以后出版的占绝大部分，共计16本，其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿，例如基础数学中的数论、代数与拓扑三本，都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点，基础数学类的书以“经典”为主，应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家，例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士，曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。

作者简介

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

图书目录

Preface

I Basic Results

1.0 Introduction

1.l Basic Concepts

1.2 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 Heily Property

4.6 Exercises

Notes

V Independent Sets and Matchings

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 HamUtonlan 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 K5 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