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代数图基础2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

刘彥佩著著
出版社：合肥：中国科学技术大学出版社
ISBN：7312030086
出版时间：2013
标注页数：402页
文件大小：55MB
文件页数：417页
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图书目录

Chapter 1 Abstract Graphs1

1.1 Graphs and Networks1

1.2 Surfaces7

1.3 Embeddings13

1.4 Abstract Representation18

1.5 Notes22

Chapter 2 Abstract Maps26

2.1 Ground Sets26

2.2 Basic Permutations28

2.3 Conjugate Axiom30

2.4 Transitive Axiom33

2.5 Included Angles37

2.6 Notes39

Chapter 3 Duality43

3.1 Dual Maps43

3.2 Deletion of an Edge48

3.3 Addition of an Edge58

3.4 Basic Transformation65

3.5 Notes67

Chapter 4 Orientability69

4.1 Orientation69

4.2 Basic Equivalence72

4.3 Euler Characteristic77

4.4 Pattern Examples80

4.5 Notes81

Chapter 5 Orientable Maps83

5.1 Butterflies83

5.2 Simplified Butterflies85

5.3 Reduced Rules88

5.4 Orientable Principles92

5.5 Orientable Genus94

5.6 Notes95

Chapter 6 Nonorientable Maps97

6.1 Barflies97

6.2 Simplified Barflies100

6.3 Nonorientable Rules102

6.4 Nonorientable Principles106

6.5 Nonorientable Genus107

6.6 Notes108

Chapter 7 Isomorphisms of Maps110

7.1 Commutativity110

7.2 Isomorphism Theorem114

7.3 Recognition117

7.4 Justification120

7.5 Pattern Examples123

7.6 Notes127

Chapter 8 Asymmetrization129

8.1 Automorphisms129

8.2 Upper Bounds of Group Order131

8.3 Determination of the Group134

8.4 Rootings138

8.5 Notes141

Chapter 9 Asymmetrized Petal Bundles143

9.1 Orientable Petal Bundles143

9.2 Planar Pedal Bundles147

9.3 Nonorientable Pedal Bundles150

9.4 The Number of Pedal Bundles154

9.5 Notes157

Chapter 10 Asymmetrized Maps159

10.1 Orientable Equation159

10.2 Planar Rooted Maps165

10.3 Nonorientable Equation171

10.4 Gross Equation175

10.5 The Number of Rooted Maps178

10.6 Notes179

Chapter 11 Maps Within Symmetry181

11.1 Symmetric Relation181

11.2 An Application182

11.3 Symmetric Principle184

11.4 General Examples186

11.5 Notes188

Chapter 12 Genus Polynomials190

12.1 Associate Surfaces190

12.2 Layer Division of a Surface192

12.3 Handle Polynomials195

12.4 Crosscap Polynomials197

12.5 Notes198

Chapter 13 Census with Partitions200

13.1 Planted Trees200

13.2 Hamiltonian Cubic Maps207

13.3 Halin Maps209

13.4 Biboundary Inner Rooted Maps211

13.5 General Maps215

13.6 Pan-Flowers217

13.7 Notes221

Chapter 14 Equations with Partitions223

14.1 The Meson Functional223

14.2 General Maps on the Sphere227

14.3 Nonseparable Maps on the Sphere230

14.4 Maps Without Cut-Edge on Surfaces233

14.5 Eulerian Maps on the Sphere236

14.6 Eulerian Maps on Surfaces239

14.7 Notes243

Chapter 15 Upper Maps of a Graph245

15.1 Semi-Automorphisms on a Graph245

15.2 Automorphisms on a Graph248

15.3 Relationships250

15.4 Upper Maps with Symmetry252

15.5 Via Asymmetrized Upper Maps254

15.6 Notes257

Chapter 16 Genera of Graphs259

16.1 A Recursion Theorem259

16.2 Maximum Genus261

16.3 Minimum Genus264

16.4 Average Genus267

16.5 Thickness272

16.6 Interlacedness275

16.7 Notes276

Chapter 17 Isogemial Graphs278

17.1 Basic Concepts278

17.2 Two Operations279

17.3 Isogemial Theorem281

17.4 Nonisomorphic Isogemial Graphs282

17.5 Notes287

Chapter 18 Surface Embeddability289

18.1 Via Tree-Travels289

18.2 Via Homology299

18.3 Via Joint Trees303

18.4 Via Configurations310

18.5 Notes316

Appendix 1 Concepts of Polyhedra,Surfaces,Embeddings and Maps318

Appendix 2 Table of Genus Polynomials for Embeddings and Maps of Small Size328

Appendix 3 Atlas of Rooted and Unrooted Maps for Small Graphs340

Bibliography388

Terminology394

Author Index400