劉彥佩編著的《代數(shù)圖基礎(chǔ)》是中國科學(xué)技術(shù)大學(xué)校友文庫之一。本書以圖的代數(shù)表示為起點，著重于多面形、曲面、嵌入和地圖等對象，用一個統(tǒng)一的理論框架，揭示在更具普遍性的組合乃至代數(shù)構(gòu)形中，可通過局部對稱性反映全局性質(zhì)。特別是通過多項式型的不變量刻畫這些構(gòu)形在不同拓?fù)�、組合和代數(shù)變換下的分類。同時，也提供這些分類在算法上的實現(xiàn)和復(fù)雜性分析。

     劉彥佩編著的《代數(shù)圖基礎(chǔ)》以圖的代數(shù)表示為起點，著重于多面形、曲面、嵌入和地圖等對象，用一個統(tǒng)一的理論框架，揭示在更具普遍性的組 合乃至代數(shù)構(gòu)形中，可通過局部對稱性反映全局性質(zhì)。特別是通過多項式型的不變量刻畫這些構(gòu)形在不同拓?fù)�、組合和代數(shù)變換下的分類。同時，也提 供這些分類在算法上的實現(xiàn)和復(fù)雜性分析。雖然本書中的結(jié)論多以作者的前期工作為基...

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