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 de ned on two cyclic groups with adjacency re-sembling twisting that is typically used in de ning 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.

Keywords: Cayley graphs, vertex-transitive graphs, non-Cayley, meta-Cayley and meta-cyclic graphs.

Quaestiones Mathematicae 34(2011), 425{431.