The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an

eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a

graph (digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and

only if v is an eccentric vertex of u in G. In this paper, we have considered an open problem. Partly we have

characterized graphs with specified maximum degree such that ED(G) = 