D-DISTANCE ON GRAPHS

For two vertices u and v of a graph G, the usual distance d (u, v), is the length of the shortest path between u and v . Chartand et al introduced the concept of detour distance by conserding the length of the longest path between u and v.Kathiresan et al introduced the concept of superior distance and signal distance. In some of these distances only the lengths of various paths were considered. By considering the degrees of various vertices present in the path, in addition to the length of the path, in this article we introduced the concept of D-distance. We study some properties of this new distance.