ALGEBRAIC GRAPH THEORY SECOND EDITIONPDF电子书下载

1 Introduction 1

part one - LINEAR ALGEBRA IN GRAPH THEORY 7

2 The spectrum of a graph 7

3 Regular graphs and line graphs 14

4 Cycles and cuts 23

5 Spanning trees and associated structures 31

6 The tree-number 38

7 Deteminant expansions 44

8 Vertex-partitions and the spectrum 52

part two COLOURING PROBLEMS 63

9 The chromatic polynomial 63

10 Subgraph expansions 73

11 The multiplicative expansion 81

12 The induced subgraph expansion 89

13 The Tutte polynomial 97

14 Chromatic polynomials and spanning trees 106

part three - SYMMETRY AND REGULARITY 115

15 Automorphisms of graphs 115

16 Vertex-transitive graphs 122

17 Symmetric graphs 130

18 Symmetric graphs of degree three 138

19 The covering-graph construction 149

20 Distance-transitive graphs 155

21 Feasibility of intersection arrays 164

22 Imprimitivity 173

23 Minimal regular graphs with given girth 180

References 191

Index 202