دانلود کتاب Topological Theory of Graphs

فهرست مطالب :

Preface to DG Edition
Preface to USTC Edition
Contents
1 Preliminaries
1.1 Sets and relations
1.2 Partitions and permutations
1.3 Graphs and networks
1.4 Groups and spaces
1.5 Notes
2 Polyhedra
2.1 Polygon double covers
2.2 Supports and skeletons
2.3 Orientable polyhedra
2.4 Non-orientable polyhedra
2.5 Classic polyhedra
2.6 Notes
3 Surfaces
3.1 Polyhegons
3.2 Surface closed curve axiom
3.3 Topological transformations
3.4 Complete invariants
3.5 Graphs on surfaces
3.6 Up-embeddability
3.7 Notes
4 Homology on Polyhedra
4.1 Double cover by travels
4.2 Homology
4.3 Cohomology
4.4 Bicycles
4.5 Notes
5 Polyhedra on the Sphere
5.1 Planar polyhedra
5.2 Jordan closed-curve axiom
5.3 Uniqueness
5.4 Straight-line representations
5.5 Convex representation
5.6 Notes
6 Automorphisms of a Polyhedron
6.1 Automorphisms of polyhedra
6.2 Eulerian and non-Eulerian codes
6.3 Determination of automorphisms
6.4 Asymmetrization
6.5 Notes
7 Gauss Crossing Sequences
7.1 Crossing polyhegons
7.2 Dehn’s transformation
7.3 Algebraic principles
7.4 Gauss crossing problem
7.5 Notes
8 Cohomology on Graphs
8.1 Immersions
8.2 Realization of planarity
8.3 Reductions
8.4 Planarity auxiliary graphs
8.5 Basic conclusions
8.6 Notes
9 Embeddability on Surfaces
9.1 Joint tree model
9.2 Associate polyhegons
9.3 A transformation
9.4 Criteria of embeddability
9.5 Notes
10 Embeddings on Sphere
10.1 Left and right determinations
10.2 Forbidden configurations
10.3 Basic order characterization
10.4 Number of planar embeddings
10.5 Notes
11 Orthogonality on Surfaces
11.1 Definitions
11.2 On surfaces of genus zero
11.3 Surface models
11.4 On surfaces of genus not zero
11.5 Notes
12 Net Embeddings
12.1 Definitions
12.2 Face admissibility
12.3 General criterion
12.4 Special criteria
12.5 Notes
13 Extremality on Surfaces
13.1 Maximal genus
13.2 Minimal genus
13.3 Shortest embedding
13.4 Thickness
13.5 Crossing number
13.6 Minimal bend
13.7 Minimal area
13.8 Notes
14 Matroidal Graphicness
14.1 Definitions
14.2 Binary matroids
14.3 Regularity
14.4 Graphicness
14.5 Cographicness
14.6 Notes
15 Knot Polynomials
15.1 Definitions
15.2 Knot diagram
15.3 Tutte polynomial
15.4 Pan-polynomial
15.5 Jones Polynomial
15.6 Notes
Bibliography
Subject Index
Author Index