Topics in Graph Automorphisms and Reconstruction

An in-depth coverage of selected areas of graph theory focusing on symmetry properties of graphs, ideal for beginners and specialists.

Josef Lauri (Author), Raffaele Scapellato (Author)

9781316610442, Cambridge University Press

Paperback / softback, published 2 June 2016

194 pages, 35 b/w illus. 155 exercises
22.7 x 15.2 x 1.2 cm, 0.3 kg

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.

Preface to the second edition
Preface to the first edition
1. Graphs and groups: preliminaries
2. Various types of graph symmetry
3. Cayley graphs
4. Orbital graphs and strongly regular graphs
5. Graphical regular representations and pseudosimilarity
6. Products of graphs
7. Special classes of vertex-transitive graphs and digraphs
8. The reconstruction conjectures
9. Reconstructing from subdecks
10. Counting arguments in vertex-reconstruction
11. Counting arguments in edge-reconstruction
References
List of notation
Index of terms and definitions.

Subject Areas: Combinatorics & graph theory [PBV], Mathematics [PB]