Lethbridge Number Theory and Combinatorics Seminar: Joy Morris

A Cayley graph Cay(G;S) has the elements of G as its vertices, with g--gs if and only if s is an element of S. There is a natural colouring of the edges of any such graph, by assigning colour s to an edge if it came from the element s of S. For a Cayley digraph, any graph automorphism that preserves this colouring has to be a group automorphism of G. For a Cayley graph, this is not the case. I will present examples of Cayley graphs that have automorphisms that do not correspond to group automorphisms of G. I will also show that for some families of groups, such examples are not possible.

I will also discuss the more general problem of automorphisms that permute the colours, rather than necessarily preserving all of them.