The Number of Subtrees of Trees with Given Degree Sequence

TL;DR

This paper explores properties of subtree counts in trees with fixed degree sequences, identifying extremal trees with the maximum number of subtrees and linking these to Wiener index minimization.

Contribution

It characterizes trees with given degree sequences that maximize the number of subtrees, extending recent findings and connecting to Wiener index optimization.

Findings

Identified trees with maximum subtrees for given degree sequences

Established partial orderings of extremal trees

Linked extremal trees to Wiener index minimization

Abstract

This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalizes the recent results of Kirk and Wang. These trees coincide with those which were proven by Wang and independently Zhang et al. to minimize the Wiener index. We also provide a partial ordering of the extremal trees with different degree sequences, some extremal results follow as corollaries.