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Graphs, Groups and Surfaces

A.T. White
Publisher: 
North Holland
Publication Date: 
2001
Number of Pages: 
364
Format: 
Hardcover
Price: 
96.95
ISBN: 
0444500758
Category: 
Textbook
BLL Rating: 

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 Chapter 1. HISTORICAL SETTING
Chapter 2. A BRIEF INTRODUCTION TO GRAPH THEORY
2-1. Definition of a Graph
2-2. Variations of Graphs
2-3. Additional Definitions
2-4. Operations on Graphs
2-5. Problems
Chapter 3. THE AUTOMORPHISM GROUP OF A GRAPH
3-1. Definitions
3-2. Operations on Permutations Groups
3-3. Computing Automorphism Groups of Graphs
3-4. Graphs with a Given Automorphism Group
3-5. Problems
Chapter 4. THE CAYLEY COLOR GRAPH OF A GROUP PRESENTATION
4-1. Definitions
4-2. Automorphisms
4-3. Properties
4-4. Products
4-5. Cayley Graphs
4-6. Problems
Chapter 5. AN INTRODUCTION TO SURFACE TOPOLOGY
5-1. Definitions
5-2. Surfaces and Other 2-manifolds
5-3. The Characteristic of a Surface
5-4. Three Applications
5-5. Pseudosurfaces
5-6. Problems
Chapter 6. IMBEDDING PROBLEMS IN GRAPH THEORY
6-1. Answers to Some Imbedding Questions
6-2. Definition of "Imbedding"
6-3. The Genus of a Graph
6-4. The Maximum Genus of a Graph
6-5. Genus Formulae for Graphs
6-6. Rotation Schemes
6-7. Imbedding Graphs on Pseudosurfaces
6-8. Other Topological Parameters for Graphs
6-9. Applications
6-10. Problems
Chapter 7. THE GENUS OF A GROUP
7-1. Imbeddings of Cayley Color graphs
7-2. Genus Formulae for Groups
7-3. Related Results
7-4. The Characteristic of a Group
7-5. Problems
Chapter 8. MAP-COLORING PROBLEMS
8-1. Definitions and the Six-Color Theorem
8-2. The Five-Color Theorem
8-3. The Four-Color Theorem
8-4. Other Map-Coloring Problems: The Heawood Map-Coloring Theorem
8-5. A Related Problem
8-6. A Four-Color Theorem for the Torus
8-7. A Nine-Color Theorem for the Torus and Klein Bottle
8-8. k-degenerate Graphs
8-9. Coloring Graphs on Pseudosurfaces
8-10. The Cochromatic Number of Surfaces
8-11. Problems
Chapter 9. QUOTIENT GRAPHS AND QUOTIENT MANIFOLDS: CURRENT GRAPHS AND THE COMPLETE GRAPH THEOREM
9-1. The Genus of Kn
9-2. The Theory of Current Graphs as Applied to Kn
9-3. A Hint of Things to Come
9-4. Problems
Chapter 10. VOLTAGE GRAPHS
10-1. Covering Spaces
10-2. Voltage Graphs
10-3. Examples
10-4. The Heawood Map-coloring Theorem (again)
10-5. Strong Tensor Products
10-6. Covering Graphs and Graphical Products
10-7. Problems
Chapter 11. NONORIENTABLE GRAPH IMBEDDINGS
11-1. General Theory
11-2. Nonorientable Covering Spaces
11-3. Nonorientable Voltage Graph Imbeddings
11-4. Examples
11-5. The Heawood Map-coloring Theorem, Nonorientable Version
11-6. Other Results
11-7. Problems
Chapter 12. BLOCK DESIGNS
12-1. Balanced Incomplete Block Designs
12-2. BIBDs and Graph Imbeddings
12-3. Examples
12-4. Strongly Regular Graphs
12-5. Partially Balanced Incomplete Block Designs
12-6. PBIBDs and Graph Imbeddings
12-7. Examples
12-8. Doubling a PBIBD
12-9. Problems
Chapter 13. HYPERGRAPH IMBEDDINGS
13-1. Hypergraphs
13-2. Associated Bipartite Graphs
13-3. Imbedding Theory for Hypergraphs
13-4. The Genus of a Hypergraph
13-5. The Heawood Map-Coloring Theorem, for Hypergraphs
13-6. The Genus of a Block Design
13-7. An Example
13-8. Nonorientable Analogs
13-9. Problems
Chapter 14. FINITE FIELDS ON SURFACES
14-1. Graphs Modelling Finite Rings
14-2. Basic Theorems About Finite Fields
14-3. The Genus of Fp
14-4. The Genus of Fpr
14-5. Further Results
14-6. Problems
Chapter 15. FINITE GEOMETRIES ON SURFACES
15-1. Axiom Systems for Geometries
15-2. n-Point Geometry
15-3. The Geometries of Fano, Pappus, and Desargues
15-4. Block Designs as Models for Geometries
15-5. Surface Models for Geometries
15-6. Fano, Pappus, and Desargues Revisited
15-7. 3-Configurations
15-8. Finite Projective Planes
15-9. Finite Affine Planes
15-10. Ten Models for AG(2,3)
15-11. Completing the Euclidean Plane
15-12. Problems
Chapter 16. MAP AUTOMORPHISM GROUPS
16-1. Map Automorphisms
16-2. Symmetrical Maps
16-3. Cayley Maps
16-4. Complete Maps
16-5. Other Symmetrical Maps
16-6. Self -Complementary Graphs
16-7. Self-dual Maps
16-8. Paley Maps
16-9. Problems
Chapter 17. ENUMERATING GRAPH IMBEDDINGS
17-1. Counting Labelled Orientable 2-Cell Imbeddings
17-2. Counting Unlabelled Orientable 2-Cell Imbeddings
17-3. The Average Number of Symmetries
17-4. Problems
Chapter 18. RANDOM TOPOLOGICAL GRAPH THEORY
18-1. Model I
18-2. Model II
18-3. Model III
18-4. Model IV
18-5. Model V
18-6. Model VI- Random Cayley Maps
18-7. Problems
Chapter 19. CHANGE RINGING
19-1. The Setting
19-2. A Mathematical Model
19-3. Minimus
19-4. Doubles
19-5. Minor
19-6. Triples and Fabian Stedman
19-7. Extents on n Bells
19-8. Summary
19-9. Problems
REFERENCES. BIBLIOGRAPHY. INDEX OF SYMBOLS. INDEX OF DEFINITIONS

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