New results on the eccentric digraphs of the digraphs

Let G be a digraph. For two vertices u and v in G, the distance d(u, v) from u to v in G is the length of the shortest directed path from u to v. The eccentricity e(v) of v is the maximum distance of v to any other vertex of G. A vertex u is an eccentric vertex of v if the distance from v to u is equal to the eccentricity of v. The eccentric digraph ED(G) of G is the digraph that has the same vertex set as G and the arc set defined by: there is an arc from u to v if and only if v is an eccentric vertex of u. In this paper, we determine the eccentric digraphs of digraphs for various families of digraphs and we get some new results on the eccentric digraphs of the digraphs.