The Terminal Wiener Index of Trees with Diameter or Maximum Degree

Abstract

The terminal Wiener index of a tree is the sum of distances for all pairs of pendent vertices, which recently arose in the study of phylogenetic tree reconstruction and the neighborhood of trees. This paper presents sharp upper and lower bounds for the terminal Wiener index in terms of its order and diameter and characterizes all extremal trees that attain these bounds. Additionally, we investigate the properties of extremal trees that attain the maximum terminal Wiener index among all trees of order \(n\) with fixed maximum degree.