Extremal Schultz Index Of Acyclic Molecular Graphs With Diameter \(4\)

Abstract

Let \(G = (V, E)\) be a simple connected graph, where \(d_u\) is the degree of vertex \(u\), and \(d_G(u, v)\) is the distance between \(u\) and \(v\). The Schultz index of \(G\) is defined as \(\mathcal{W}_+(G) = \sum\limits_{u,v \subset V(G)} (d_u + d_v)d_G(u,v).\)In this paper, we investigate the Schultz index of a class of trees with diameter not more than \(4\).