A bound involving the centroid and Wiener index of a tree

Abstract

In this short note it is shown that for any tree T of order n, (formula presented), where σ(Τ) is the Wiener index of T , c is in its centroid, and bw(c) is the branch weight at c. It provides a companion result to the upper bound (formula presented), shown by Barefoot, Entringer, and Székely.