Directable Zeros in a Binary Matrix

A binary matrix whose O's are such that corresponding to any 0 in the matrix all its positions along at least one of the four directions are also 0' s is called a four -directable binary matrix. This matrix is characterized in this paper in terms of the adjacency matrix of a digraph, having an overlap base interval representation which is a generalized concept of an overlap interval representation. A base interval is an ordered pair(S_v,p_v} where S_v is an interval on the real line and p_v is a point of S_v. Instead of taking the overlap representation if we consider the intersection, representation then its adjacency matrix reduces to a particular form of 4 -directable binary matrix.