The competition-common enemy graph of a digraph

The competition graph of a digraph was first defined in 1968 by Cohen in the study of ecosystems. The competition graph essentially relates any two species which have a common prey.In this paper, a competition-common enemy graph of a digraph is defined and studied. As the term suggests, it relates any two species which have a common prey and a common enemy. Results analogous to those found for competition graphs are obtained.