• Gd-DISTANCE IN GRAPHS

Abstract

The distance between two vertices u and v in a graph is the number of edges in a shortest path connecting them. This is also known as the geodesic distance. In this paper we introduce the concept of Gd-distance by considering the degrees of various vertices presented in the path, in addition to the distance of the path we study some properties with this new distance. We define the eccentricities of vertices, radius and diameter of G with respect to the Gd-distance. First we prove that the new distance is a metric on the set of vertices of G. We compare the geodesic distance and Gd-distance of two vertices u, v of V.