AN INTERVAL DIGRAPH IN RELATION TO ITS ASSOCIATED BIPARTITE GRAPH

The intersection digraph of a family of ordered pairs of sets {(S(v), T(v)): v is-an-element-of V} is the digraph D(V,E) such that uv is-an- element-of E if and only if S(u) and T(v) not-equal empty set. Interva l digraphs are those intersection digraphs for which the subsets are i ntervals on the real line. In a previous paper, they were characterize d in terms of Ferrers digraphs and a close relationship, was obtained between an interval digraph and a digraph of Ferrers dimension 2. In o rder to characterize a digraph D of Ferrers dimension 2, Cogis associa ted an undirected graph H(D) with D in a suitable way, the vertices of H(D) corresponding to the zeros of the adjacency matrix of D. He prov ed that D has Ferrers dimension at most 2 if and only if H(D) is bipar ite. Depending on the above characterization, this paper first obtains some properties of a digraph of Ferrers dimension 2; then it is shown how the notion of interior edges is related to an interval digraph.