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刘彥佩编著的《代数图基础》以图的代数表示为起点，着重于多面形、
曲面、嵌入和地图等对象，用一个统一的理论框架，揭示在更具普遍性的组 合乃至代数构形中，可通过局部对称性反映全局性质。特别是通过多项式型
的不变量刻画这些构形在不同拓扑、组合和代数变换下的分类。同时，也提 供这些分类在算法上的实现和复杂性分析。虽然本书中的结论多以作者的前
期工作为基...
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| 內容簡介： |
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刘彥佩编著的《代数图基础》是中国科学技术大学校友文库之一。本书以图的代数表示为起点，着重于多面形、曲面、嵌入和地图等对象，用一个统一的理论框架，揭示在更具普遍性的组合乃至代数构形中，可通过局部对称性反映全局性质。特别是通过多项式型的不变量刻画这些构形在不同拓扑、组合和代数变换下的分类。同时，也提供这些分类在算法上的实现和复杂性分析。
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| 目錄：
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Preface to the USTC Alumni’S Series
Preface
Chapter 1 Abstract Graphs
1．1 Graphs and Networks
1．2 Surfaces
1．3 Embeddings
1．4 Abstract Representation
1．5 Nores
Chapter 2 Abstract Maps
2．1 Ground Sets
2．2 Basic Permutations
2．3 Conjugate Axiom
2．4 nansitive Axiom
2．5 Included Angles
2．6 Notes
Chapter 3 Duality
3．1 Dual Maps
3．2 Deletion of an Edge
3．3 Addition of an Edge
3．4 Basic Transformation
3．5 Nores
Chapter 4 Orientability
4.1 Orientation
4.2 Basic Equivalence
4.3 Euler Characteristic
4.4 Pattern Examples
4.5 Notes
Chapter 5 Orientable Maps
5.1 Butterflies
5.2 Simplified Butterflies
5.3 Reduced Rules
5.4 Orientable Principles
5.5 Orientable Genus
5.6 Notes
Chapter 6 Nonorientable Maps
6.1 Barflies
6.2 Simplified Barflies
6.3 Nonorientable Rules
6.4 Nonorientable Principles
6.5 Nonorientable Genus
6.6 Notes
Chapter 7 Isomorphisms of Maps
7.1 Commutativity
7.2 Isomorphism Theorem
7.3 Recognition
7.4 Justification
7.5 Pattern Examples
7.6 Notes
Chapter 8 Asymmetrization
8.1 Automorphisms
8.2 Upper Bounds of Group Order
8.3 Determination of the Group
8.4 Rootings
8.5 Notes
Chapter 9 Asymmetrized Petal Bundles
9.1 Orientable Petal Bundles
9.2 Planar Pedal Bundles
9.3 Nonorientable Pedal Bundles
9.4 The Number of Pedal Bundles
9.5 Notes
Chapter 10 Asymmetrized Maps
10.1 Orientable Equation
10.2 Planar Rooted Maps
10.3 Nonorientable Equation
10.4 Gross Equation
10.5 The Number of Rooted Maps
10.6 Notes
Chapter 11 Maps Within Symmetry
11.1 Symmetric Relation
11.2 An Application
11.3 Symmetric Principle
11.4 General Examples
11.5 Notes
Chapter 12 Genus Polynomials
12.1 Associate Surfaces
12.2 Layer Division of a Surface
12.3 Handle Polynomials
12.4 Crosscap Polynomials
12.5 Notes
Chapter 13 Census with Partitions
13.1 Planted Trees
13.2 Hamiltonian Cubic Maps
13.3 Halin Maps
13.4 Biboundary Inner Rooted Maps
13.5 General Maps
13.6 Pan-Flowers
13.7 Notes
Chapter 14 Equations with Partitions
14.1 The Meson Functional
14.2 General Maps on the Sphere
14.3 Nonseparable Maps on the Sphere
14.4 Maps Without Cut-Edge on Surfaces
14.5 Eulerian Maps on the Sphere
14.6 Eulerian Maps on Surfaces
14.7 Notes
Chapter 15 Upper Maps of a Graph
15.1 Semi-Automorphisms on a Graph
15.2 Automorphisms on a Graph
15.3 Relationships
15.4 Upper Maps with Symmetry
15.5 Via Asymmetrized Upper Maps
15.6 Notes
Chapter 16 Genera of Graphs
16.1 A Recursion Theorem
16.2 Maximum Genus
16.3 Minimum Genus
16.4 Average Genus
16.5 Thickness
16.6 Interlacedness
16.7 Notes
Chapter 17 Isogemial Graphs
17.1 Basic Concepts
17.2 Two Operations
17.3 Isogemial Theorem
17.4 Nonisomorphic Isogemial Graphs
17.5 Notes
Chapter 18 Surface Embeddability
18.1 Via Tree-Travels
18.2 Via Homology
18.3 Via Joint Trees
18.4 Via Configurations
18.5 Notes
Appendix 1 Concepts of Polyhedra, Surfaces, Embeddings and
Maps
Appendix 2 Table of Genus Polynomials for Embeddings and Maps of
Small Size
Appendix 3 Atlas of Rooted and Unrooted Maps for Small
Graphs
Bibliography
Terminology
Author Index
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