代数图基础

　　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

　　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。