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图论基础
  • 张海良，苏岐芳，林荣斐编著 著
  • 出版社： 北京：清华大学出版社
  • ISBN：9787302241638
  • 出版时间：2011
  • 标注页数：115页
  • 文件大小：4MB
  • 文件页数：122页
  • 主题词：图论

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图书目录

Chapter 1 Basic concepts1

1.1 Graph and simple graph1

1.2 Graph operations3

1.3 Isomorphism7

1.4 Incident and adjacent matrix7

1.5 The spectrum of graph10

1.6 The spectrum of several graphs16

1.7 Results from matrix theory19

1.8 About the largest zero of characteristic polynomials22

1.9 Spectrum radius28

Chapter 2 path and cycle30

2.1 The path30

2.2 The cycle33

2.3 The diameter of a graph and its complement graph36

Chapter 3 Tree39

3.1 Tree39

3.2 Spanning tree41

3.3 A bound for the tree number of regular graphs47

3.4 Cycle space and bound space of a graph48

Chapter 4 Connectivity51

4.1 Cut edges51

4.2 Cut vertex52

4.3 Block55

4.4 Connectivity57

Chapter 5 Euler and Hamilton graphs60

5.1 Euler path and circuits60

5.2 Hamilton graph62

Chapter 6 Matching and matching polynomial66

6.1 Matching66

6.2 Bipartite graph and perfect matching67

6.3 Matching polynomial69

6.4 The relation between spectrum and matching polynomial72

6.5 Relation between several graphs74

6.6 Several matching equivalent and matching unique graphs75

6.7 The Hosoya index of several graphs76

6.8 Two trees with minimal Hosoya index79

6.9 Recent results in matching83

Chapter 7 Laplacian and Quasi-Laplacian spectrum85

7.1 Sigma function85

7.2 The spanning tree and sigma function87

7.3 Quasi-Laplacian Spectrum88

7.4 Basic lemmas89

7.5 Main results90

7.6 Three different spectrum of regular graphs96

Chapter 8 More theorems form matrix theory100

8.1 The irreducible matrix100

8.2 Cauchy's interlacing theorem102

8.3 The eigenvalues of A(G)and graph structure103

Chapter 9 Chromatic polynomial105

9.1 Induction105

9.2 Two different formula for chromatic polynomial107

9.3 Chromatic polynomials for several type of graphs109

9.4 Estimate the color number110

References112

Bibliography115

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