Vertex-transitive closures of graphs

Abstract

A vertex-transitive closure of $\hat{I}“$ is a vertex-transitive supergraph of $\hat{I}“$ on the same vertex set. The vertex-transitive number of a graph $\hat{I}“$, denoted by $d_{vt}(\hat{I}“)$, is the smallest integer for which there exists a $d_{vt}(\hat{I}“)$-regular vertex-transitive closure of $\hat{I}“$. In this paper we use various algebraic and combinatorial methods to study vertex-transitive closures of graphs and the associated vertex-transitive number.

8 pages, 3 figures