图的拓扑理论

图书标准信息

• 作者 刘彦佩 著
• 出版社 中国科学技术大学出版社
• 出版时间 2008-09
• 版次 1
• ISBN 9787312022753
• 定价 88.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 458页
• 字数 400千字
• 正文语种 英语
• 丛书 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

【内容简介】

本书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。
本书可作为基础数学，应用数学、系统科学、计算机科学等专业高年级本科生和研究生的补充教材，也可供相关专业的教师和科研工作者参考。

【目录】

Preface
Chapter1Preliminaries
1.1Setsandrelations
1.2Partitionsandpermutations
1.3Graphsandnetworks
1.4Groupsandspaces
1.5Notes

Chapter2Polyhedra
2.1Polygondoublecovers
2.2Supportsandskeletons
2.3Orientablepolyhedra
2.4Nonorientablepolyhedra
2.5Classicpolyhedra
2.6Notes

Chapter3Surfaces
3.1Polyhegons
3.2Surfaceclosedcurveaxiom
3.3Topologicaltransformations
3.4Completeinvariants
3.5Graphsonsurfaces
3.6Up-embeddability
3.7Notes

Chapter4HomologyonPolyhedra
4.1Doublecoverbytravels
4.2Homology
4.3Cohomology
4.4Bicycles
4.5Notes

Chapter5PolyhedraontheSphere
5.1Planarpolyhedra
5.2Jordanclosedcurveaxiom
5.3Uniqueness
5.4Straightlinerepresentations
5.5Convexrepresentation
5.6Notes

Chapter6AutomorphismsofaPolyhedron
6.1Automorphisms
6.2V-codesandF-codes
6.3Determinationofautomorphisms
6.4Asymmetrization
5.5Notes

Chapter7GaussCrossingSequences
7.1Crossingpolyhegons
7.2Dehnstransformation
7.3Algebraicprinciples
7.4GaussCrossingproblem
7.5Notes

Chapter8CohomologyonGraphs
8.1Immersions
8.2Realizationofplanarity
8.3Reductions
8.4Planarityauxiliarygraphs
8.5Basicconclusions
8.6Notes
Contents

Chapter9EmbeddabilityonSurfaces
9.1Jointtreemodel
9.2Associatepolyhegons
9.3Theexchanger
9.4Criteriaofembeddability
9.5Notes

Chapter10EmbeddingsontheSphere
10.1Leftandrightdeterminations
10.2Forbiddenconfigurations
10.3Basicordercharacterization
10.4Numberofplanarembeddings
10.5Notes

Chapter11OrthogonalityonSurfaces
11.1Definitions
11.2Onsurfacesofgenuszero
11.3SurfaceModel
11.4Onsurfacesofgenusnotzero
11.5Notes

Chapter12NetEmbeddings
12.1Definitions
12.2Faceadmissibility
12.3Generalcriterion
12.4Specialcriteria
12.5Notes

Chapter13ExtremalityonSurfaces
13.1Maximalgenus
13.2Minimalgenus
13.3Shortestembedding
13.4Thickness
13.5Crossingnumber
13.6Minimalbend
13.7Minimalarea
13.8Notes

Chapter14MatroidalGraphicness
14.1Definitions
14.2Binarymatroids
14.3Regularity
14.4Graphicness
14.5Cographicness
14.6Notes

Chapter15KnotPolynomials
15.1Definitions
15.2Knotdiagram
15.3Tuttepolynomial
15.4Pan-polynomial
15.5Jonespolynomial
15.6Notes
Bibliography
SubjectIndex
AuthorIndex