Details

Autor(en) / Beteiligte

• White, Arthur T

Titel

Graphs of groups on surfaces : interactions and models [electronic resource]

Auflage

1st ed

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references (p. 351-352) and indexes.
• Cover; Contents; 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 Topology5-1. 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 graphs7-2. 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 Theorem9-1. The Genus of K?; 9-2. The Theory of Current Graphs as Applied to K?; 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. Examples11-5. 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
• The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English
• English