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 andmaps
appendix 2 table of genus polynomials for embeddings and maps ofsmall size
appendix 3 atlas of rooted and unrooted maps for smallgraphs
bibliography
terminology
author index