作者：Chris Godsil，Gordon
页数：19,439页
出版社：世界图书出版公司
出版日期：2004
ISBN：9787506266185
电子书格式：pdf/epub/txt
内容简介
本书是“Springer数学研究生丛书”（GTM）之207，其中主要论述代数与图论之间的关系，阅读本书只需具备线性代数及群论方面的基础知识，因此本书不仅适用于图论、组合数学和离散数学领域的研究生及研究人员，也适用于相关专业的高年级本科生。
作者简介
C.Godsil，加拿大滑铁卢大学（University of Waterloo）组合数学与优化系（department of combinatorics and optimization)教授。滑铁卢大学是一所以研究为主的中等大小的公立大学，创建于1957年。
目录
Preface
1 Graphs
1.1 Graphs
1.2 Subgraphs
1.3 Automorphisms
1.4 Homomorphisms
1.5 Circulant Graphs
1.6 Johnson Graphs
1.7 Line Graphs
1.8 Planar Graphs
Exercises
Notes
References
2 Groups
2.1 Permutation Groups
2.2 Counting
2.3 Asymmetric Graphs
2.4 Orbits on Pairs
2.5 Primitivity
2.6 Primitivity and Connectivity
Exercises
Notes
References
3 Transitive Graphs
3.1 Vertex-Transitive Graphs
3.2 Edge-Transitive Graphs
3.3 Edge Connectivity
3.4 Vertex Connectivity
3.5 Matchings
3.6 Hamilton Paths and Cycles
3.7 Cayley Graphs
3.8 Directed Cayley Graphs with No Hamilton Cycles
3.9 Retracts
3.10 Transpositions
Exercises
Notes
References
4 Arc-Transitive Graphs
4.1 Arc-Transitive Graphs
4.2 Arc Graphs
4.3 Cubic Arc-Transitive Graphs
4.4 The Petersen Graph
4.5 Distance-Transitive Graphs
4.6 The Coxeter Graph
4.7 Tutte’s 8-Cage
Exercises
Notes
References
5 Generalized Polygons and Moore Graphs
5.1 Incidence Graphs
5.2 Projective Planes
5.3 A Family of Projective Planes
5.4 Generalized Quadrangles
5.5 A Family of Generalized Quadrangles
5.6 Generalized Polygons
5.7 Two Generalized Hexagons
5.8 Moore Graphs
5.9 The Hoffman-Singleton Graph
5.10 Designs
Exercises
Notes
References
6 Homomorphisms
6.1 The Basics
6.2 Cores
6.3 Products
……
7 Kneser Graphs
8 Matrix Theory
9 Interlacing
10 Strongly Regular Graphs
11 Two-Graphs
12 Line Graphs and Eigenvalues
13 The Laplacian of a Graph
14 Cuts and Flows
15 The Rank Polynomial
16 Knots
17 Knots and Eulerian Cycles
Glossary of Symbols
Index
1 Graphs
1.1 Graphs
1.2 Subgraphs
1.3 Automorphisms
1.4 Homomorphisms
1.5 Circulant Graphs
1.6 Johnson Graphs
1.7 Line Graphs
1.8 Planar Graphs
Exercises
Notes
References
2 Groups
2.1 Permutation Groups
2.2 Counting
2.3 Asymmetric Graphs
2.4 Orbits on Pairs
2.5 Primitivity
2.6 Primitivity and Connectivity
Exercises
Notes
References
3 Transitive Graphs
3.1 Vertex-Transitive Graphs
3.2 Edge-Transitive Graphs
3.3 Edge Connectivity
3.4 Vertex Connectivity
3.5 Matchings
3.6 Hamilton Paths and Cycles
3.7 Cayley Graphs
3.8 Directed Cayley Graphs with No Hamilton Cycles
3.9 Retracts
3.10 Transpositions
Exercises
Notes
References
4 Arc-Transitive Graphs
4.1 Arc-Transitive Graphs
4.2 Arc Graphs
4.3 Cubic Arc-Transitive Graphs
4.4 The Petersen Graph
4.5 Distance-Transitive Graphs
4.6 The Coxeter Graph
4.7 Tutte’s 8-Cage
Exercises
Notes
References
5 Generalized Polygons and Moore Graphs
5.1 Incidence Graphs
5.2 Projective Planes
5.3 A Family of Projective Planes
5.4 Generalized Quadrangles
5.5 A Family of Generalized Quadrangles
5.6 Generalized Polygons
5.7 Two Generalized Hexagons
5.8 Moore Graphs
5.9 The Hoffman-Singleton Graph
5.10 Designs
Exercises
Notes
References
6 Homomorphisms
6.1 The Basics
6.2 Cores
6.3 Products
……
7 Kneser Graphs
8 Matrix Theory
9 Interlacing
10 Strongly Regular Graphs
11 Two-Graphs
12 Line Graphs and Eigenvalues
13 The Laplacian of a Graph
14 Cuts and Flows
15 The Rank Polynomial
16 Knots
17 Knots and Eulerian Cycles
Glossary of Symbols
Index
