Symmetry in Graphs

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.

List of contents

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.

About the author

Ted Dobson is Professor at the University of Primorska, Slovenia.Aleksander Malnič is Professor at the University of Ljubljana.Dragan Marušič is Professor at the University of Primorska, Slovenia and the founder of the Slovenian school in Algebraic Graph Theory.

Summary

This is the first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory. Suitable for graduate students, it goes from basic material on vertex-transitive graphs and permutation group theory right up to the field's major open problems, and includes many examples and exercises illustrating the theory.

Product details

• Authors: Ted Dobson, Ted (Univerza Na Primorskem Dobson, Aleksander Malni¿, Aleksander (Univerza na Primorskem Malnic, Aleksander Malnič, Dragan Maru¿i¿, Dragan (Univerza na Primorskem Marusic, Dragan Marušič
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.05.2022
• EAN: 9781108429061
• ISBN: 978-1-108-42906-1
• No. of pages: 450
• Series: Cambridge Studies in Advanced Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Social sciences, law, business > Media, communication > Communication science; Algebra, COMPUTERS / Information Theory, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Discrete Mathematics, MATHEMATICS / Algebra / General, MATHEMATICS / Combinatorics, Algebraic Geometry, Discrete Mathematics, Combinatorics & graph theory, Information theory, Combinatorics and graph theory