A survey on eccentric digraph of a (di)graph

Abstract

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 survey we take a look on the progress made till date in the theory of Eccentric digraphs of graphs and digraphs, in general. And list the open problems in the area.