20. 5. 2022
The book »Symmetry in Graphs« was published by Cambridge University Press in the series Cambridge Studies in Advanced Mathematics. Authors of this first full-length book on the major theme of symmetry in graphs are Ted Dobson, Aleksander Malnič and Dragan Marušič, researchers of the University of Primorska.
Books within the Cambridge Studies in Advanced Mathematics series aim to introduce the reader to an active area of mathematical research. Besides being suitable for graduate students, the treatments are applicable for experts from other branches of mathematics, seeking access to research topics.
ABOUT »Symmetry in Graphs«
The book begins with the basic material, leading the reader towards major problems and most active research themes of this fast-growing field, which forms a part of algebraic graph theory. Authors motivate the detailed discussion of individual topics that follow the introduction.
It is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques. Investigations of the field shed new light on permutation groups and related algebraic structures.
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.
REVIEWS
»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
More about the publication can be found here.