Graphs, groups, and surfaces

Arthur T. White (Eds.)9780444876430, 044487643X

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 of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as “difficult”.

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Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Foreword to the First Edition
Pages v-vi
A.T. W.

Foreword to the Second Edition
Pages vii-viii
A.T. W.

Chapter 1 Historical Setting
Pages 1-4

Chapter 2 A Brief Introduction to Graph Theory
Pages 5-13

Chapter 3 The Automorphism Group of a Graph
Pages 15-21

Chapter 4 The Cayley Color Graph of a Group Presentation
Pages 23-38

Chapter 5 An Introduction to Surface Topology
Pages 39-56

Chapter 6 Imbedding Problems in Graph Theory
Pages 57-82

Chapter 7 The Genus of a Group
Pages 83-99

Chapter 8 Map-Coloring Problems
Pages 101-124

Chapter 9 Quotient Graphs and Quotient Manifolds (and Quotient groups!)
Pages 125-155

Chapter 10 Voltage Graphs
Pages 157-176

Chapter 11 Nonorientable Graph Imbeddings
Pages 177-188

Chapter 12 Block Designs
Pages 189-204

Chapter 13 Hypergraph Imbeddings
Pages 205-218

Chapter 14 Map Automorphism Groups
Pages 219-256

Chapter 15 Change Ringing
Pages 257-277

References
Pages 279-302

Bibliography
Pages 303-304

Index of Symbols
Pages 305-307

Index of Definitions
Pages 309-314