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.

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 Friday, January 11, 2013