A fuzzy graph-based Kulli–Basava descriptor for isomer discrimination and physicochemical property prediction

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Abstract In this paper, a generalized fuzzy Kulli-Basava index ( $$FKB^{*}_1$$ ) of fuzzy graphs is introduced, which is an extension of the classical index, by introducing a fuzzy vertex degree, fuzzy edge membership value, and fuzzy sum of the degree of incident vertices. Unlike existing fuzzy topological descriptors such as the fuzzy Randić index ( $$\textrm{FR}$$ ) and fuzzy first Zagreb index ( $$\textrm{FZ}_1$$ ), which rely solely on endpoint degrees, $$FKB^{*}_1$$ incorporates $$I_e(v)$$ , a vertex-weight that aggregates fuzzy degrees of neighbours and reaches two bonds into the molecular environment, thereby capturing richer structural information. When considering binary membership, the index reduces to $$KB_1$$ and is found to perfectly discriminate between isomers in the case of the three alkane families (hexane, heptane, and octane), outperforming all classical indices, with the exception of assigning distinct values to most isomers of octane. QSPR analysis demonstrates exceptional correlation with acentric factor and strong performance for entropy. The computational algorithm ensures efficiency for molecular graphs, and the index is most effective within fixed carbon chain lengths for properties related to the molecular branching. $$FKB^{*}_1$$ is a powerful molecular descriptor but is not a complete graph invariant.

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