图的拓扑理论 pdf epub mobi txt 电子书 下载 2025

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《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。

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
……
chapter 9　embeddability on surfaces
chapter 10 embeddings on the sphere
chapter 11 orthogonality on surfaces
chapter 12 net embeddings
chapter 13 extremality on surfaces
chapter 14 matroial graphicness
chapter 15 knot polynomials
bibliography
subject index
author index
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