SEMINAR: Groups and Combinatorics Seminar: Colour-preserving automorphisms of Cayley graphs

Speaker: Gabriel Verret (University of Auckland)

Time and place: 16:00 Friday 03/03/2017 in Weatherburn LT

Title: Colour-preserving automorphisms of Cayley graphs

Abstract: A Cayley digraph Cay(G,S) comes equipped with a natural colouring of its arcs: the arc (g,sg) has colour s. It is an easy exercise to show that the group of colour-preserving automorphisms of the graph is exactly G. If the digraph is actually a graph, one can forget about the orientation of the arcs and colour the edges instead: the edge {g,sg} has colour {s,s^(-1)}. Determining the group of colour-preserving automorphisms in this case is much harder. This is the subject of this talk, with a specific focus on the case when the colour-preserving group does not normalise G.