Optimal Behaviour in Extremal Bounds for $σ$-Irregularity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917365215657984 |
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| author | Hamoud, Jasem Abdullah, Duaa |
| author_facet | Hamoud, Jasem Abdullah, Duaa |
| contents | 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 $σ(G)=\sum_{uv\in E(G)}(d_G(u)-d_G(v))^2$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06845 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Behaviour in Extremal Bounds for $σ$-Irregularity Hamoud, Jasem Abdullah, Duaa Combinatorics 05C05, 05C12, 05C20, 05C25, 05C35, 05C76, 68R10 G.2.2 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 $σ(G)=\sum_{uv\in E(G)}(d_G(u)-d_G(v))^2$. 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. |
| title | Optimal Behaviour in Extremal Bounds for $σ$-Irregularity |
| topic | Combinatorics 05C05, 05C12, 05C20, 05C25, 05C35, 05C76, 68R10 G.2.2 |
| url | https://arxiv.org/abs/2510.06845 |