代数图基础PDF电子书下载

Chapter 1 Abstract Graphs 1

1.1 Graphs and Networks 1

1.2 Surfaces 7

1.3 Embeddings 13

1.4 Abstract Representation 18

1.5 Notes 22

Chapter 2 Abstract Maps 26

2.1 Ground Sets 26

2.2 Basic Permutations 28

2.3 Conjugate Axiom 30

2.4 Transitive Axiom 33

2.5 Included Angles 37

2.6 Notes 39

Chapter 3 Duality 43

3.1 Dual Maps 43

3.2 Deletion of an Edge 48

3.3 Addition of an Edge 58

3.4 Basic Transformation 65

3.5 Notes 67

Chapter 4 Orientability 69

4.1 Orientation 69

4.2 Basic Equivalence 72

4.3 Euler Characteristic 77

4.4 Pattern Examples 80

4.5 Notes 81

Chapter 5 Orientable Maps 83

5.1 Butterflies 83

5.2 Simplified Butterflies 85

5.3 Reduced Rules 88

5.4 Orientable Principles 92

5.5 Orientable Genus 94

5.6 Notes 95

Chapter 6 Nonorientable Maps 97

6.1 Barflies 97

6.2 Simplified Barflies 100

6.3 Nonorientable Rules 102

6.4 Nonorientable Principles 106

6.5 Nonorientable Genus 107

6.6 Notes 108

Chapter 7 Isomorphisms of Maps 110

7.1 Commutativity 110

7.2 Isomorphism Theorem 114

7.3 Recognition 117

7.4 Justification 120

7.5 Pattern Examples 123

7.6 Notes 127

Chapter 8 Asymmetrization 129

8.1 Automorphisms 129

8.2 Upper Bounds of Group Order 131

8.3 Determination of the Group 134

8.4 Rootings 138

8.5 Notes 141

Chapter 9 Asymmetrized Petal Bundles 143

9.1 Orientable Petal Bundles 143

9.2 Planar Pedal Bundles 147

9.3 Nonorientable Pedal Bundles 150

9.4 The Number of Pedal Bundles 154

9.5 Notes 157

Chapter 10 Asymmetrized Maps 159

10.1 Orientable Equation 159

10.2 Planar Rooted Maps 165

10.3 Nonorientable Equation 171

10.4 Gross Equation 175

10.5 The Number of Rooted Maps 178

10.6 Notes 179

Chapter 11 Maps Within Symmetry 181

11.1 Symmetric Relation 181

11.2 An Application 182

11.3 Symmetric Principle 184

11.4 General Examples 186

11.5 Notes 188

Chapter 12 Genus Polynomials 190

12.1 Associate Surfaces 190

12.2 Layer Division of a Surface 192

12.3 Handle Polynomials 195

12.4 Crosscap Polynomials 197

12.5 Notes 198

Chapter 13 Census with Partitions 200

13.1 Planted Trees 200

13.2 Hamiltonian Cubic Maps 207

13.3 Halin Maps 209

13.4 Biboundary Inner Rooted Maps 211

13.5 General Maps 215

13.6 Pan-Flowers 217

13.7 Notes 221

Chapter 14 Equations with Partitions 223

14.1 The Meson Functional 223

14.2 General Maps on the Sphere 227

14.3 Nonseparable Maps on the Sphere 230

14.4 Maps Without Cut-Edge on Surfaces 233

14.5 Eulerian Maps on the Sphere 236

14.6 Eulerian Maps on Surfaces 239

14.7 Notes 243

Chapter 15 Upper Maps of a Graph 245

15.1 Semi-Automorphisms on a Graph 245

15.2 Automorphisms on a Graph 248

15.3 Relationships 250

15.4 Upper Maps with Symmetry 252

15.5 Via Asymmetrized Upper Maps 254

15.6 Notes 257

Chapter 16 Genera of Graphs 259

16.1 A Recursion Theorem 259

16.2 Maximum Genus 261

16.3 Minimum Genus 264

16.4 Average Genus 267

16.5 Thickness 272

16.6 Interlacedness 275

16.7 Notes 276

Chapter 17 Isogemial Graphs 278

17.1 Basic Concepts 278

17.2 Two Operations 279

17.3 Isogemial Theorem 281

17.4 Nonisomorphic Isogemial Graphs 282

17.5 Notes 287

Chapter 18 Surface Embeddability 289

18.1 Via Tree-Travels 289

18.2 Via Homology 299

18.3 Via Joint Trees 303

18.4 Via Configurations 310

18.5 Notes 316

Appendix 1 Concepts of Polyhedra,Surfaces,Embeddings and Maps 318

Appendix 2 Table of Genus Polynomials for Embeddings and Maps of Small Size 328

Appendix 3 Atlas of Rooted and Unrooted Maps for Small Graphs 340

Bibliography 388

Terminology 394

Author Index 400