Topics in Graph Automorphisms and Reconstruction (London Mathematical Society Lecture Note Series, Series Number 432)

This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. The final four chapters are devoted to the reconstruction problem, and here special emphasis is given to those results that involve the symmetry of graphs, many of which are not to be found in other books. This second edition expands on several of the topics found in the first edition and includes both an enriched bibliography and a wide collection of exercises. Clearer proofs are provided, as are new examples of graphs with interesting symmetry properties. Any student who masters the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem.

Josef Lauri is a Professor in the Department of Mathematics at the University of Malta. His main areas of research interest are in graph reconstruction and related problems in graph symmetries, and in colouring problems of mixed hypergraphs.

Raffaele Scapellato is a Professor in the Department of Mathematics at Politecnico di Milano in Italy. His research interests mostly concern graph theory, and he has a strong background in algebra.