The extremal values of the Wiener index of a tree with given degree sequence

TL;DR

This paper characterizes trees with given degree sequences that achieve extremal Wiener index values, providing insights into their structure and potential applications in chemistry.

Contribution

It introduces a complete characterization of trees with specified degree sequences that attain maximum and minimum Wiener index values.

Findings

Identifies trees with extremal Wiener index for given degree sequences.

Provides structural characterization of these extremal trees.

Enhances understanding of graph descriptors in chemical graph theory.

Abstract

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. The tree that minimizes the Wiener index among trees of given maximal degree was studied. We characterize trees that achieve the maximum and minimum Wiener index, given the number of vertices and the degree sequence.