The Terminal Wiener Index of Trees with Diameter or Maximum Degree

TL;DR

This paper establishes sharp bounds for the terminal Wiener index of trees based on order, diameter, and maximum degree, and characterizes extremal trees that attain these bounds, relevant for phylogenetics.

Contribution

It provides new bounds and characterizations for the terminal Wiener index in trees considering diameter and maximum degree, advancing understanding in graph theory and phylogenetics.

Findings

Sharp upper and lower bounds for the terminal Wiener index based on order and diameter.

Characterization of extremal trees attaining these bounds.

Analysis of trees with fixed maximum degree maximizing the terminal Wiener index.

Abstract

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