Description
Book SynopsisThis is the first full-length book on the major theme of symmetry in graphs. Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques. In practice the street goes both ways and these investigations shed new light on permutation groups and related algebraic structures. The book assumes a first course in graph theory and group theory but no specialized knowledge of the theory of permutation groups or vertex-transitive graphs. It begins with the basic material before introducing the field''s major problems and most active research themes in order to motivate the detailed discussion of individual topics that follows. Featuring many examples and over 450 exercises, it is an essential introduction to the field for graduate students and a valuable addition to any algebraic graph theorist''s bookshelf.
Trade Review'The book is an excellent introduction to graph symmetry, assuming only first courses in each of group theory and graph theory. Illustrative and instructive examples of graphs with high symmetry are given along with motivating problems. The theory of group actions is interspersed throughout the book, as appropriate to the development of the graph story, and there are separate chapters treating different research directions, for example, vertex-transitive graphs and their automorphism groups, the Cayley Isomorphism Problem, and Hamiltonicity. The book provides a seamless entry for students and other interested people into this fascinating study of the interplay between symmetry and network theory, with extensive lists of exercises at the end of each chapter, and important research problems on graph symmetry discussed throughout the book, and especially in the final chapter.' Cheryl Praeger, University of Western Australia, Perth
'Dobson, Malnič and Marušič have done us a real service. They offer a thorough treatment of graph symmetry, the first text book on the topic. What makes this even more useful is that their treatment is detailed, careful and gentle.' Chris Godsil, University of Waterloo, Ontario
'A book like this is long overdue. It brings together a vast array of important and interesting material about graph symmetries, and is very well presented. Congratulations to the authors on a fine achievement.' Marston Conder, University of Auckland
Table of Contents1. Introduction and constructions; 2. The Petersen graph, blocks, and actions of A5; 3. Some motivating problems; 4. Graphs with imprimitive automorphism group; 5. The end of the beginning; 6. Other classes of graphs; 7. The Cayley isomorphism problem; 8. Automorphism groups of vertex-transitive graphs; 9. Classifying vertex-transitive graphs; 10. Symmetric graphs; 11. Hamiltonicity; 12. Semiregularity; 13. Graphs with other types of symmetry: Half-arc-transitive graphs and semisymmetric graphs; 14. Fare you well; References; Author index; Index of graphs; Index of symbols;Index of terms.
