On non-Cayley vertex-transitive graphs and the meta-Cayley graphs

Abstract

The pursuit to identify vertex-transitive non-Cayley graphs has been deliberate for some time now. In that vein, Alspach and Parsons [1] introduced metacirculant graphs. They are defined on two cyclic groups with adjacency resembling twisting that is typically used in defining semi-direct products of groups. In this sequel we generalise the construction to general groups and introduce a class of graphs we call meta-Cayley graphs.