Minimum Weighted Szeged Index Trees

TL;DR

This paper introduces new methods to analyze and identify trees with the minimum weighted Szeged index, providing explicit examples and conjectures about their structure.

Contribution

It presents a novel approach to characterize minimum weighted Szeged index trees and offers the first explicit trees with up to 81 vertices.

Findings

Identified trees with minimal weighted Szeged index up to 81 vertices

Proposed conjectures on the structural properties of these trees

Developed new analytical tools for weighted Szeged index analysis

Abstract

Weighted Szeged index is a recently introduced extension of the well-known Szeged index. In this paper, we present a new tool to analyze and characterize minimum weighted Szeged index trees. We exhibit the best trees with up to 81 vertices and use this information, together with our results, to propose various conjectures on the structure of minimum weighted Szeged index trees.