When the arc-colored line digraph of a cayley colored digraph is again a cayley colored digraph

Abstract

Let D6(G) be the Cayley colored ügraph of a finite group G generated by A. The arc-colored line digraph of a Cayley colored digraph ie obtained by appropriately coloring the arcs of its line digraph. In this paper it is shown that the group of automorphisms of D6 (G) that act as permutations on the color classes is isomorphic to the gemidirect product of G a¡rd a particular subgroup of AutG. Neceeeary and sufficient conditions for the arc-colored üne digraph of a Cayley colored digraph ¿lso to be a Cayley colored digraph are then derived.