THE ECCENTRIC DIGRAPH OF THE CORONA OF C-n WITH K-m, C-m OR P-m

Let G be a graph with a set of vertices V(G) and a set of edges E(G). The distance from vertex u to vertex upsilon in G, denoted by d(u;upsilon),is the length of the shortest path from vertex u to upsilon. The eccentricity of vertex u in graph G is the maximum distance from vertex u to any other vertices in G, denoted by e(u). Vertex upsilon is an eccentric vertex from u if d(u;upsilon) = e(u). The eccentric digraph ED(G) of a graph G is a graph that has the same set of vertices as G, and there is an arc(directed edge) joining vertex u to upsilon if upsilon is an eccentric vertex from u. In this paper, we answer the open problem proposed by Boland and Miller [1] to find the eccentric digraph of various classes of graphs.In particular,we determine the eccentric digraph of the corona of C-n with K-m; C-m and P-m, with C-n;K-m or P-m are cycle, complete graph and path,respectively.