The Steiner Wiener index of trees with given diameter

Abstract

The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as (Equation presented) where dg(u,v) is the distance between vertices u and v of G. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S C V(G), the Steiner distance dg(S) of the vertices of 5 is the minimum size of connected subgraphs whose vertex set is S. We now introduce the concept of the Steiner Wiener index of a graph. The Steiner k-Wiener index SWk(G) of G is defined by (Equation presented). In this paper, we study the expressions or bounds for SWk(G) with diameter 3,4, n - 2, respectively. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.