Topics in graph automorphisms and reconstruction

Abstract

In this second edition of our book we have tried to maintain the same structure as the first edition, namely a text which, although not providing an exhaustive coverage of graph symmetries and reconstruction, provides a detailed coverage of some particular areas (generally motivated by our own research interest), which is not a haphazard collection of results but which presents a clear pathway through this thick forest. And our aim remains that of producing a text which can relatively quickly guide the reader to the point of being able to understand and carry out research in the topics which we cover. Among the additions in this edition we point out the use of the free computer programs GAP, GRAPE and Sage to construct and investigate some well-known graphs, including examples with properties like being semisymmetric, a topic which was treated in the first edition but for which examples are not easy to construct ‘by hand’. We have also updated some chapters with new results, improved the presentation and proofs of others, and introduced short treatments of topics such as character theory of abelian groups and their Cayley graphs to emphasise the connection between graph theory and other areas of mathematics. We have corrected a number of errors which we found in the first edition, and for this we would like to thank colleagues who have pointed out several of them, particularly Bill Kocay, Virgilio Pannone and Alex Scott.