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图论导引
图论导引

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数理化

  • 电子书积分:14 积分如何计算积分?
  • 作 者:〔美〕GaryChartrand,PingZhang著
  • 出 版 社:人民邮电出版社
  • 出版年份:2006
  • ISBN:7115148341
  • 页数:448 页
图书介绍:本书介绍了图论的常用主题,同时也包含一些尚需进一步研究或未解决的议题。
《图论导引》目录
标签:导引

1.Introduction 1

1.1.Graphs and Graph Models 1

1.2.Connected Graphs 9

1.3.Common Classes of Graphs 19

1.4.Multigraphs and Digraphs 26

2.Degrees 31

2.1.The Degree of a Vertex 31

2.2.Regular Graphs 38

2.3.Degree Sequences 43

2.4.Excursion:Graphs and Matrices 48

2.5.Exploration:Irregular Graphs 50

3.Isomorphic Graphs 55

3.1.The Definition of Isomorphism 55

3.2.Isomorphism as a Relation 63

3.3.Excursion:Graphs and Groups 66

3.4.Excursion:Reconstruction and Solvability 76

4.Trees 85

4.1.Bridges 85

4.2.Trees 87

4.3.The Minimum Spanning Tree Problem 94

4.4.Excursion:The Number of Spanning Trees 101

5.Connectivity 107

5.1.Cut-Vertices 107

5.2.Blocks 111

5.3.Connectivity 115

5.4.Menger’s Theorem 124

5.5.Exploration:Geodetic Sets 130

6.Traversability 133

6.1.Eulerian Graphs 133

6.2.Hamiltonian Graphs 140

6.3.Exploration:Hamiltonian Walks and Numbers 152

6.4.Excursion:The Early Books of Graph Theory 156

7.Digraphs 161

7.1.Strong Digraphs 161

7.2.Tournaments 169

7.3.Excursion:Decision-Making 176

7.4.Exploration:Wine Bottle Problems 180

8.Matchings and Factorization 183

8.1.Matchings 183

8.2.Factorization 194

8.3.Decompositions and Graceful Labelings 209

8.4.Excursion:Instant Insanity 214

8.5.Excursion:The Petersen Graph 219

8.6.Exploration:γ-Labelings of Graphs 224

9.Planarity 227

9.1.Planar Graphs 227

9.2.Embedding Graphs on Surfaces 241

9.3.Excursion:Graph Minors 249

9.4.Exploration:Embedding Graphs in Graphs 253

10.Coloring 259

10.1.The Four Color Problem 259

10.2.Vertex Coloring 267

10.3.Edge Coloring 280

10.4.Excursion:The Heawood Map Coloring Theorem 288

10.5.Exploration:Local Coloring 293

11.Ramsey Numbers 297

11.1.The Ramsey Number of Graphs 297

11.2.Turan’s Theorem 307

11.3.Exploration:Rainbow Ramsey Numbers 314

11.4.Excursion:Erdos Numbers 321

12.Distance 327

12.1.The Center of a Graph 327

12.2.Distant Vertices 333

12.3.Excursion:Locating Numbers 341

12.4.Excursion:Detour and Directed Distance 346

12.5.Exploration:Channel Assignment 351

12.6.Exploration:Distance Between Graphs 357

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