ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 69,   1   (2000)
pp.   59-70

COMPARING A CAYLEY DIGRAPH WITH ITS REVERSE
M. ABAS

Abstract.  A Cayley digraph $G=C(\Gamma,X)$ for a group $\Gamma$ and a generating set $X$ is the digraph with vertex set $V(G)=\Gamma$ and arcs $(g,gx)$ where $g\in\Gamma$ and $x\in X$. The reverse of $C(\Gamma,X)$ is the Cayley digraph $G^-1=C(\Gamma,X^-1)$ where $X^-1=\x^-1; x\in X\$. We are interested in sufficient conditions for a Cayley digraph not to be isomorphic to its reverse and focus on Cayley digraphs of metacyclic groups with small generating sets.

AMS subject classification.  05C25
Keywords.  Cayley digraph, digraph isomorphism