A graph is vertex-transitive if its group of automorphism acts transitively on its vertices. A very important concept in the study of these graphs is that of local action, that is, the permutation group induced by a vertex-stabilizer on the corresponding neighbourhood. I will explain some of its importance and discuss some attempts to generalize it to the case of directed graphs.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
