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arXiv · 2510.06845

Optimal Behaviour in Extremal Bounds for $\sigma$-Irregularity

Jasem Hamoud·Duaa Abdullah
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Abstract

In this paper, we establishe the extremal bounds of the topological indices -- Sigma index -- focusing on analyzing the sharp upper bounds and the lower bounds of the Sigma index, which is known $\sigma(G)=\sum_{uv\in E(G)}(d_G(u)-d_G(v))^2$. We establish precise lower and upper bounds for the Sigma index, leveraging a non-increasing degree sequence $\mathscr{D} = (d_1, d_2, \dots, d_n)$, A fundamental challenge in the study of topological indices lies in establishing precise bounds, as such findings illuminate intrinsic relationships among diverse indices.

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Jasem Hamoud, Duaa Abdullah. 2025-10-08. Optimal Behaviour in Extremal Bounds for $\sigma$-Irregularity. https://arxiv.org/abs/2510.06845

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