SEMINAR: Groups and Combinatorics Seminar, Graphs and transitivity on 2-geodesics

Alice Devillers (UWA)

will speak on

Graphs and transitivity on 2-geodesics

at 3pm Friday January the 17th in Blakers Lecture Theatre.

Abstract :

Joint work with Wei Jin, Cai Heng Li, Cheryl Praeger, Akos Seress.

An s-geodesic in a graph is a shortest path connecting two vertices at distance s. We say that a graph is locally transitive on s-geodsics if the stabiliser of any vertex is transitive on the s-geodesics starting at that vertex. Being locally transitive on s-geodesic is not a monotone property: if an automorphism group G of a graph is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. For instance, (local) transitivity on 2-geodesics does not imply local transitivity on arcs (1-geodesics).

In this talk, I will first show a nice characterisation of all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics.

Then I will describe graphs that are (locally) transitive on 2-geodesics and on arcs, in terms of their local structure.