Topological Indices Among Strong Support Vertex

TL;DR

This paper investigates the irregularity properties of trees with strong support vertices by analyzing topological indices like the Albertson and Sigma indices, establishing bounds and extremal properties for these indices.

Contribution

It introduces new extremal bounds and irregularity properties for trees with strong support vertices, focusing on the Albertson and Sigma indices, and characterizes extremal trees within degree sequence classes.

Findings

Established extremal bounds for Albertson and Sigma indices.

Identified trees with minimal irregularity within degree classes.

Provided explicit formulas for indices of certain tree classes.

Abstract

In this paper, we provide the irregularity properties of trees with strong support vertex by analyzing two prominent topological indices: the Albertson index and the Sigma index. We further establish extremal bounds for both indices across families of trees defined by given degree sequences. Let $T_1$ and $T_2$ be a star trees of order $n$, where $T_1 \cong T_2$, then, we provide Albertson index of $T_1 \cong T_2$. Let $\mathcal{T}_{n, \Delta}$ be a class of trees with $n$ vertices, there are a tree $T^{\prime} \in \mathcal{T}_{n, \Delta}$ such that $\irr(T^{\prime}) < \irr(T)$.