| 词条 | 图的拓扑理论 |
| 释义 | 图书信息出版社: 中国科学技术大学出版社; 第1版 (2008年9月1日) 外文书名: Topological Theory on Graphs 丛书名: 当代科学技术基础理论与前沿问题研究丛书:中国科学技术大学校友文库"十一五"国家重点图书 平装: 458页 正文语种: 英语 开本: 16 ISBN: 9787312022753, 7312022758 条形码: 9787312022753 尺寸: 23.6 x 16.8 x 2.6 cm 重量: 721 g 内容简介《图的拓扑理论》不在于图的拓扑性质本身，而是着意以图为代表的一些组合构形为出发点，揭示与拓扑学中一些典型对蠏，如多面形、曲面、嵌入、纽结等的联系，特别是显示了定理有效化的途径对于以拓扑学为代表的基础数学的作用。同时，也提出了一些新的曲面模型，为超大规模集成电路的布线尝试构建多方面的理论基础。 目录Preface Chapter 1 Preliminaries 1.1 Sets and relations 1.2 Partitions and permutations 1.3 Graphs and networks 1.4 Groups and spaces 1.5 Notes Chapter 2 Polyhedra 2.1 Polygon double covers 2.2 Supports and skeletons 2.3 Orientable polyhedra 2.4 Nonorientable polyhedra 2.5 Classic polyhedra 2.6 Notes Chapter 3 Surfaces 3.1 Polyhegons 3.2 Surface closed curve axiom 3.3 Topological transformations 3.4 Complete invariants 3.5 Graphs on surfaces 3.6 Up-embeddability 3.7 Notes Chapter 4 Homology on Polyhedra 4.1 Double cover by travels 4.2 Homology 4.3 Cohomology 4.4 Bicycles 4.5 Notes Chapter 5 Polyhedra on the Sphere 5.1 Planar polyhedra 5.2 Jordan closed curve axiom 5.3 Uniqueness 5.4 Straight line representations 5.5 Convex representation 5.6 Notes Chapter 6 Automorphisms of a Polyhedron 6.1 Automorphisms 6.2 V-codes and F-codes 6.3 Determination of automorphisms 6.4 Asymmetrization 5.5 Notes Chapter 7 Gauss Crossing Sequences 7.1 Crossing polyhegons 7.2 Dehn's transformation 7.3 Algebraic principles 7.4 Gauss Crossing problem 7.5 Notes Chapter 8 Cohomology on Graphs 8.1 Immersions 8.2 Realization of planarity 8.3 Reductions 8.4 Planarity auxiliary graphs 8.5 Basic conclusions 8.6 Notes Contents Chapter 9 Embeddability on Surfaces 9.1 Joint tree model 9.2 Associate polyhegons 9.3 The exchanger 9.4 Criteria of embeddability 9.5 Notes Chapter 10 Embeddings on the Sphere 10.1 Left and right determinations 10.2 Forbidden configurations 10.3 Basic order characterization 10.4 Number of planar embeddings 10.5 Notes Chapter 11 Orthogonality on Surfaces 11.1 Definitions 11.2 On surfaces of genus zero 11.3 Surface Model 11.4 On surfaces of genus not zero 11.5 Notes Chapter 12 Net Embeddings 12.1 Definitions 12.2 Face admissibility 12.3 General criterion 12.4 Special criteria 12.5 Notes Chapter 13 Extremality on Surfaces 13.1 Maximal genus 13.2 Minimal genus 13.3 Shortest embedding 13.4 Thickness 13.5 Crossing number 13.6 Minimal bend 13.7 Minimal area 13.8 Notes Chapter 14 Matroidal Graphicness 14.1 Definitions 14.2 Binary matroids 14.3 Regularity 14.4 Graphicness 14.5 Cographicness 14.6 Notes Chapter 15 Knot Polynomials 15.1 Definitions 15.2 Knot diagram 15.3 Tutte polynomial 15.4 Pan-polynomial 15.5 Jones polynomial 15.6 Notes Bibliography Subject Index Author Index |
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