A comparative study of sum-connectivity and product-connectivity Gourava indices for benzenoid hydrocarbons

Abstract

This study evaluates the sum-connectivity ($SGO$) and product-connectivity ($PGO$) Gourava indices as molecular descriptors for benzenoid hydrocarbons. Using a dataset of 30 benzenoid structures, we compare least-squares regression models for predicting $\pi$-electronic energies ($E_{\pi }$) and find that $SGO$ yields a markedly better fit than $PGO$ across molecular edge types. The indices are further assessed using three validation designs: (i) correlation analysis, in which $SGO$ exhibits strong yet non-perfect inverse correlations with standard descriptors ($M_1,M_2,SO,DSO,$ and $ABS$; $r\in [-0.9923,-0.8936]$), suggesting complementary structural information; (ii) degeneracy analysis on Octane, Nonane, and order-$10$ tree datasets, where $SGO$ attains low degeneracy rates (22.22\%, 40.00\%, and 42.45\%); and (iii) structure-sensitivity analysis on trees of order $n=10$, showing 74\% higher sensitivity than $DSO$ while maintaining a high structure-abruptness ratio ($SA=0.474386$). Overall, $SGO$ offers a favorable balance between discriminative power and numerical stability, supporting its applicability in QSPR modeling and related theoretical studies.

15 pages, 6 figures