ABSTRACT
A digraph D is strongly unipathic if it has exactly one directed path from any vertex to any other. We show that the only bicliques in such a digraph are claws, and so it follows that the claw cover, biclique cover and biclique partition numbers of D are all equal. Equivalently, the term, Boolean and nonnegative integer ranks of its adjacency matrix A(D) are all equal. We extend the unipathic property to sets of vertex disjoint paths, and prove that the above ranks are all equal to the ordinary real rank of A(D). Also, in the course of the paper, we survey a number of useful characterizations of directed versions of the clique covering and partition numbers that recur in Pullman's work.
