Diametral Reachable Index (DRI) of a Vertex

Abstract

ABSTRACT:Every graph has one or more diametral paths. A diametral path of a graph is a shortest path whose length is equal to the diameter of the graph. Let be a diametral vertex. There may be one or more diametral paths originating from . We want to find all the diametral paths, originating from . The total number of diametral paths reachable from a vertex is called the Diametral Reachable Index of that vertex, denoted . For any vertex , the , if there are no diametral paths reachable from , else we write , where is the total number of diametral paths reachable from vertex . An algorithm is developed to find DRI of each vertex of a graph, by modifying the DFS algorithm.