On The Upper Bound Of Wiener Index Of Trees And Graphs With Given Vertices And Radius

Let G be a connected graph of order n. The Wiener index W(G) of a graph G is the sum of all pairwise distances between vertices of the graph G. In this paper, we give an upper bound on Wiener index of trees and graphs with vertex number n, and radius r = 2, and characterize the extremal graphs. Moreover, we present another upper bound on Wiener index of trees with vertex number n, and radius r.