- 作 者：刘彥佩著
- 出 版 社：合肥：中国科学技术大学出版社
- 出版年份：2013
- ISBN：7312030086
- 标注页数：402 页
- PDF页数：417 页
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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