Joy Morris
University of Lethbridge
Regular representations: graphs, digraphs, oriented graphs, and coloured graphs
Abstract
Over the years, many researchers have studied the question of whether a given category of objects contains a regular representation of a group; that is, there is an object in that category admitting a regular (sharply transitive) action of the group. I will give an overview of the work that has been done on this for the categories of graphs, digraphs, and oriented graphs (an oriented graph is a digraph with no digons). I will also discuss a closely-related question for edge-coloured graphs: under what circumstances do only affine maps preserve the edge-colouring?