Characterising star-transitive and st(edge)-transitive graphs

Michael Giudici, Cai Heng Li, Akos Seress and Anne Thomas

Abstract

Recent work of Lazarovich provides necessary and sufficient conditions on a graph $L$ for there to exist a unique simply-connected $(k,L)$-complex. The two conditions are symmetry properties of the graph, namely star-transitivity and st(edge)-transitivity. In this paper we investigate star-transitive and st(edge)-transitive graphs by studying the structure of the vertex and edge stabilisers of such graphs. We also provide new examples of graphs that are both star-transitive and st(edge)-transitive.