On the Gutman-Milovanović index and chemical applications

The determination of upper and lower bounds for topological indices in molecular graphs provides critical insights into the structural properties of chemical compounds. These bounds facilitate the estimation of the ranges of topological indices based on molecular structural parameters. This study presents novel inequalities for the Gutman-Milovanović index, which generalizes several significant indices such as the first and second Zagreb indices, the Randić index, the harmonic index, the geometric-arithmetic index, the general second Zagreb index, and the general sum-connectivity index. Moreover, we derive and characterize extremal graphs for many of these inequalities. Additionally, we explore the application of the Gutman-Milovanović index in modeling the physicochemical properties of 22 polycyclic aromatic hydrocarbons. Our results demonstrate that the topological index $M_{\alpha ,\beta }$ provides accurate predictions for these properties, with $R^2$ values ranging from 0.9406 to 0.9983, indicating a strong correlation between the index and experimental data. The findings underscore the versatility of $M_{\alpha ,\beta }$ in chemical applications.