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 ${\mathcal{W}}_{+}(G)=\sum _{u,v\subset V(G)}(d_u+d_v)d_G(u,v).$In this paper, we investigate the Schultz index of a class of trees with diameter not more than $4$.