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arXiv · 2605.06695

Sharp Bounds and Extremal Fuzzy Graphs for the Fuzzy Sombor Index

Jasem Hamoud
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Abstract

The fuzzy Sombor index applies the classical Sombor index to fuzzy graphs, incorporating both edge membership values and fuzzy vertex degrees. For $\alpha>1$, the general fuzzy Sombor index it is defined as \[ \mathrm{SO}^{\mu}_{\alpha}(\Gamma)=\sum_{uv\in V(\Gamma)} \left( \mu(u,v)\, \sqrt{\mu_u^2+\mu_v^2} \right)^{\alpha}. \] This paper analyses extremal features of $\mathrm{SO}^{\mu}$ across different types of fuzzy graphs. We determine the maximum value (resp. minimum value) of $\mathrm{SO}^{\mu}$ characterise in regular fuzzy graph. We established significant inequality between the fuzzy Sombor index and other well-known fuzzy topological indices.

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Jasem Hamoud. 2026-05-04. Sharp Bounds and Extremal Fuzzy Graphs for the Fuzzy Sombor Index. https://arxiv.org/abs/2605.06695

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