Algebraic Elements of Graphs 1st Edition by Yanpei Liu ISBN 3110480735 9783110480733

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ISBN 10: 3110480735 
ISBN 13: 9783110480733
Author: Yanpei Liu

Algebraic Elements of Graphs 1st Table of contents:

1 Abstract Graphs
1.1 Graphs and networks
1.2 Surfaces
1.3 Embedding
1.4 Abstract representation
1.5 Notes
2 Abstract Maps
2.1 Ground sets
2.2 Basic permutations
2.3 Conjugate axiom
2.4 Transitive axiom
2.5 Included angles
2.6 Notes
3 Duality
3.1 Dual maps
3.2 Deletion of an edge
3.3 Addition of an edge
3.4 Basic transformation
3.5 Notes
4 Orientability
4.1 Orientation
4.2 Basic equivalence
4.3 Euler characteristic
4.4 Pattern examples
4.5 Notes
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
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
7 Isomorphisms of Maps
7.1 Commutativity
7.2 Isomorphism theorem
7.3 Recognition
7.4 Justification
7.5 Pattern examples
7.6 Notes
8 Asymmetrization
8.1 Automorphisms
8.2 Upper bounds of group order
8.3 Determination of the group
8.4 Rootings
8.5 Notes
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
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
11 Maps within Symmetry
11.1 Symmetric relation
11.2 An application
11.3 Symmetric principle
11.4 General examples
11.5 Notes
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
13 Census with Partitions
13.1 Planted trees
13.2 Hamiltonian cubic map
13.3 Halin maps
13.4 Biboundary inner rooted maps
13.5 General maps
13.6 Pan-flowers
13.7 Notes
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 the surfaces
14.7 Notes
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
16 Genera of a Graph
16.1 Recursion theorem
16.2 Maximum genus
16.3 Minimum genus
16.4 Average genus
16.5 Thickness
16.6 Interlacedness
16.7 Notes
17 Isogemial Graphs
17.1 Basic concepts
17.2 Two operations
17.3 Isogemial theorem
17.4 Non-isomorphic isogemial graphs
17.5 Notes
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
A1.1 Polyhedra
A1.2 Surfaces
A1.3 Embeddings
A1.4 Maps
Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size
A2.1 Triconnected cubic graphs
A2.2 Bouquets
A2.3 Wheels
A2.4 Link bundles
A2.5 Complete bipartite graphs
Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs
A3.1 Bouquets Bm of size 4 ≥ m ≥ 1
A3.2 Link bundles Lm, 6 ≥ m ≥ 3
A3.3 Complete bipartite graphs Km,n, 4 ≥ m, n ≥ 3
A3.4 Wheels Wn, 5 ≥ n ≥ 4

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Tags: Yanpei Liu, Algebraic Elements