COMPARING A CAYLEY DIGRAPH WITH ITS REVERSE

A Cayley digraph G = C( ;X) for a group and a generating set X is the digraph with vertex set V (G) = and arcs ( g;gx) where g 2 and x2 X. The reverse of C( ;X) is the Cayley digraph G 1 = C( ;X 1) where X 1 =fx 1 ;x2 Xg. We are interested in sucient conditions for a Cayley digraph not to be isomorphic to its reverse and focus on Cayley digraphs of metacyclic groups with small generating sets.