Characterising star-transitive and st(edge)-transitive graphs
Michael Giudici, Cai Heng Li, Akos Seress, Anne Thomas
TL;DR
This paper explores the structural properties of star-transitive and st(edge)-transitive graphs, providing new examples and analyzing their symmetry conditions to understand their role in the existence of certain simply-connected complexes.
Contribution
It investigates the structure of vertex and edge stabilisers in star- and st(edge)-transitive graphs and introduces new examples of such graphs.
Findings
Characterisation of stabiliser structures in these graphs
New examples of star- and st(edge)-transitive graphs
Insights into symmetry conditions for complex existence
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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Taxonomy
TopicsFinite Group Theory Research · Topological and Geometric Data Analysis · Geometric and Algebraic Topology