SEMINAR: Groups and Combinatorics Seminar: On distance, geodesic and arc transitivity of graphs

Groups and Combinatorics Seminar

Wei Jin (UWA)

will speak on

On distance, geodesic and arc transitivity of graphs

at 1pm in MLR 2 on Tuesday 30th of November

Abstract:

We compare three transitive properties of finite graphs. An s-arc is a vertex sequence (v_0,v_1,...,v_s) such that v_i, v_{i+1} are adjacent and v_{j-1} is not equal to v_{j+1} for each i=0,1,...,s-1 and j=1,2,...,s-1; it is also an s-geodesic if v_0 and v_s are at distance s. For s in {1,2,3}, we give an infinite family of graphs that are transitive on s-arcs and on t-geodesics for all 0< t < diam(Gamma)+1, but intransitive on (s+1)-arcs. We exhibit an infinite family of distance transitive graphs that are not 2-geodesic transitive. Finally we classify all 2-geodesic transitive graphs of prime valency that are not 2-arc transitive: the examples comprise an infinite family of non-bipartite antipodal distance transitive double covers of complete graphs. This is a joint work with Alice Devillers, Caiheng Li and Cheryl Praeger.

All welcome.