《圖論教程》是2011年科學出版社出版的圖書，作者是巴拉克里什南。
基本介紹
- 書名：圖論教程
- 作者：巴拉克里什南
- ISBN：9787030313850
- 定價： 66.00元
- 出版社：科學出版社
- 出版時間：2011年6月1日
- 開本：16開
內容簡介,作者簡介,圖書目錄,
內容簡介
這次科學出版社購買了著作權，一次影印了23本施普林格出版社出版的數學書，就是一件好事，也是值得繼續做下去的事情。大體上分一下，這23本書中，包括基礎數學書5本，套用數學書6本與計算數學書12本，其中有些書也具有交叉性質。這些書都是很新的，2000年以後出版的占絕大部分，總計16本，其餘的也是1990年以後出版的。這些書可以使讀者較快地了解數學某方面的前沿，例如基礎數學中的數論、代數與拓撲三本，都是由該領域大數學家編著的“數學百科全書”的分冊。對從事這方面研究的數學家了解該領域的前沿與全貌很有幫助。按照學科的特點，基礎數學類的書以“經典”為主，套用和計算數學類的書以“前沿”為主。這些書的作者多數是國際知名的大數學家，例如《拓撲學》一書的作者諾維科夫是俄羅斯科學院的院士，曾獲“菲爾茲獎”和“沃爾夫數學獎”。這些大數學家的著作無疑將會對我國的科研人員起到非常好的指導作用。
作者簡介
作者：（印度）巴拉克里什南（R.Balakrishnan） （印度）K.Ranganathan
圖書目錄
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
