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Does anyone know of any expository articles on Cayley graphs? I have some background in both group theory and graph theory, and know a little bit of algebraic topology. In particular, I am hoping to find an expository article which explores the graph theory point of view for Cayley graphs, ideally something which starts from the basics, and then goes on to explain some open problems. Does anybody know if anything like this exists?

Thank you in advance.

EDIT: To be more specific, by "graph theory" point of view, I mean something which has as its primary focus the graph theoretic properties of Cayley graphs, such as what is known about hamiltonicity, etc. It would be nice to know what properties of Cayley graphs translate to interesting (deliberately vague) properties of groups.

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  • $\begingroup$ Could you expand on what you mean by graph theory point of view? Are you look more for finite groups, or infinite groups (finite or infinite cayley graphs). There is an interesting conjecture about vertex transitive graphs contain Hamiltonian paths, for which Cayley graphs would be a special case of. You can also ask which graphs are quasi-isometric to Cayley graphs (it is known that there are graphs which are not). $\endgroup$ – Paul Plummer Oct 26 '15 at 20:43
  • $\begingroup$ @PaulPlummer Edited to add more context. Primarily I would like the focus to be on graph theoretic properties as opposed to group theory, although seeing how the two relate would be nice. $\endgroup$ – Ben Sheller Oct 26 '15 at 21:01
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The book "Graph symmetry: algebraic methods and applications" (eds: Hahn and Sabidussi) has several expository articles. The chapter by Alspach and the chapter by Heydemann especially focus on Cayley graphs. The book is old though - from 1996.

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