UID:
almahu_9947367839902882
Format:
1 online resource (329 p.)
Edition:
Completely rev. and enl. ed.
ISBN:
1-281-78819-8
,
9786611788193
,
0-08-087119-4
Series Statement:
North-Holland mathematics studies ; 8
Content:
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three o
Note:
Description based upon print version of record.
,
Front Cover; Graphs, Groups and Surfaces; Copyright Page; Table of 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 Permutation Groups; 3-3. Computing Automorphism Groups of Graphs; 3-4. Graphs with a Given Automorphism Group; 3-5. Other Groups of a Graph; 3-6. Problems; Chapter 4. The Cayley Color Graph of a Group Presentation; 4-1. Definitions
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4-2. Automorphisms4-3. 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. Two 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. Edmonds' Permutation Technique; 6-7. Imbedding Graphs on Pseudosurfaces
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6-8. Other Topological Parameters for Graphs6-9. 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; 8.2. The Four-color Conjecture; 8.3. The Five-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
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8.9. Coloring Graphs on Pseudosurfaces8.10. The Cochromatic Number of Surfaces; 8.11. Problems; Chapter 9. Quotient Graphs and Quotient Manifolds; 9.1. The Genus of Kn; 9.2. The Theory of Quotient Graphs and Quotient Manifolds. as Applied to Kn; 9.3. The Genus of Kn (again); 9.4. Extending the Theory; 9.5. The General Theory; 9.6. Applications to Known Imbeddings; 9.7. New Applications; 9.8. 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. Problems
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Chapter 11. Nonorientable Graph Imbeddings11.1. 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
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13-1. Hypergraphs
,
English
Additional Edition:
ISBN 0-444-87643-X
Language:
English
