Symmetry in Graphs

The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

Ted Dobson (Author), Aleksander Malni? (Author), Dragan Maruši? (Author)

9781108429061, Cambridge University Press

Hardback, published 12 May 2022

450 pages
23.5 x 15.7 x 3 cm, 0.91 kg

'There is a great amount of novelty in this book … The book has a very large number of examples and exercises. The authors use notable examples to motivate questions and test conjectures.' Pablo Spiga, MathSciNet

This 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.

1. 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.

Subject Areas: Combinatorics & graph theory [PBV], Algebraic geometry [PBMW], Algebra [PBF], Discrete mathematics [PBD], Information theory [GPF]