Regularities of Typical Sigma Index on Caterpillar Trees of Pendent Vertices

TL;DR

This paper investigates the properties of the Sigma index on caterpillar trees, revealing its relationship with the Albertson index and providing models for analyzing such trees in chemical graph theory.

Contribution

It introduces a detailed study of the Sigma index on caterpillar trees and demonstrates its correlation with the Albertson index, offering efficient modeling approaches.

Findings

Strong correlation between Sigma and Albertson indices.

Models for topological indices on caterpillar trees.

Insights applicable to chemical graph theory.

Abstract

In this paper, topological indices play a significant role in the analysis of caterpillar trees, especially due to their applications in chemical graph theory. We presented a study on topological indices related to the Sigma index, which we carefully selected on caterpillar trees with multiple levels. Through the election of these topological indices, we provide efficient models of these indices on caterpillar trees, as it is known that the Albertson index is the basis on which most of the topological indices are built and we have shown this through the close correlation between the Albertson's index and the Sigma index.