SEMINAR: Groups and Combinatorics Seminar: Locally triangular graphs and rectagraphs with symmetry

Groups and Combinatorics Seminar

Joanna Fawcett (UWA)

will speak on

Locally triangular graphs and rectagraphs with symmetry

at 3pm on Friday 15 of August in Weatherburn LT

Abstract: Locally triangular graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-arc lies in a unique quadrangle. A graph is locally rank 3 if it has a group of automorphisms G such that for each vertex u, the permutation group induced by the vertex stabiliser of u in G on the neighbourhood of u is transitive of rank 3. One natural place to seek locally rank 3 graphs is among locally triangular graphs. In this talk, we will discuss our classification of the connected locally triangular graphs that are also locally rank 3, which we obtain by classifying the locally 4-homogeneous rectagraphs (with some additional structure). This is joint work with J. Bamberg, A. Devillers and C. Praeger.