Double vertex digraphs of digraphs

Abstract

a b s t r a c tLet D be a digraph of order n. The double vertex digraph S 2 (D) of D is the digraph whose vertex set consists of all ordered pairs of distinct vertices of V (D) such that there is an arc in S 2 (D) from (x, y) to (u, v) if and only if x = u and there is an arc in D from y to v, or y = v and there is an arc in D from x to u. In this paper, we establish some relationships between a digraph and its double vertex digraph.