Graph automorphism groups: reference request

Question

I would like to find something like dictionary that contains info about graph automorphisms groups. Recently have found "Algebraic Graph Theory" by Godsil but I cannot find something similar in this book. I assume that good references exist. I will be grateful for any comments.

Answer 1

I can suggest "Godsil, Chris, and Gordon F. Royle. Algebraic graph theory. Vol. 207. Springer Science & Business Media, 2001" which contains a complete chapter about graphs and groups, covering automorphisms of graphs.

For a nice overview on Algebraic Graph Theory in general, I have enjoyed "Knauer, Ulrich, and Kolja Knauer. Algebraic graph theory: morphisms, monoids and matrices. Vol. 41. Walter de Gruyter GmbH & Co KG, 2019."

I've also found the following book, which I haven't read yet but it looks promising: "Lauri, Josef, and Raffaele Scapellato. Topics in graph automorphisms and reconstruction. Vol. 432. Cambridge University Press, 2016."

Answer 2

The book "Introduction to Graph Theory" by Behzad and Chartrand has a chapter on Automorphism groups of Graphs. Among other things they prove Frucht's theorem, which states that every finite group is the full automorphism group of some graph. Perhaps you would find a good introduction there.