SEMINAR: Groups and Combinatorics Seminar: Carlisle King, 4pm Aug 30 in Weatherburn LT

Speaker: Carlisle King (University of Western Australia)

Title: Edge-primitive 3-arc-transitive graphs

Time and place: 4pm Friday 30 Aug 2019, Weatherburn LT

Abstract: Let Gamma be a finite simple graph with G = Aut(Gamma). We say that Gamma is edge-primitive if G acts primitively on the edges of Gamma. An s-arc in Gamma is an ordered path of length s. We say that Gamma is s-arc-transitive if G is transitive on the set of s-arcs of Gamma.

In 1981, Weiss proved that there exists no finite s-arc-transitive graph of valency at least 3 for s geq 8. Since then, there has been considerable effort to characterise s-arc-transitive graphs for s leq 7. One interesting family of graphs is that of edge-primitive graphs. Many famous graphs are edge-primitive, such as the Heawood graph and the Higman-Sims graph. In 2011, Li and Zhang classified finite edge-primitive s-arc-transitive graphs for s geq 4. We study the problem of classifying finite edge-primitive 3-arc-transitive graphs. This is joint work with Michael Giudici.