A Mathematical Medley

A graph is vertex-transitive if its group of automorphism acts transitively on its vertices. In other words, all the vertices are "equivalent" with respect to the structure of the graph. A very important concept in the study of these graphs is that of local action, that is, the permutation group induced by a vertex-stabiliser on the corresponding neighbourhood. I will explain some of the reasons for the importance of this concept in this area.