Volume :6 , Issue :4 ,Page :135-140

Abstract :The diametral path of a graph is the shortest path between two vertices which has length equal to diameter of that graph. Vertex - disjoint diametral path set of a graph is introduced as a collection of vertex - disjoint diametral paths of a graph so that every vertex of the graph appears in exactly one diametral path. Vertex - disjoint diametral path number d v is the cardinality of such a set. The vertex - disjoint diametral path index D v is the number of such sets that can be formed for a graph. In this paper, a few results on d v and D v in certain classes of graphs are presented and characterization is made for the graphs which admit this property.