Optimizing predictive models for evaluating the F-temperature index in predicting the π-electron energy of polycyclic hydrocarbons, applicable to carbon nanocones

In the fields of mathematics, chemistry, and the physical sciences, graph theory plays a substantial role. Using modern mathematical techniques, quantitative structure-property relationship (QSPR) modeling predicts the physical, synthetic, and natural properties of substances based only on their chemical composition. For a chemical graph, the temperature of a vertex is a local property introduced by Fajtlowicz (1988). A temperature-based graphical descriptor is structured based on temperatures of vertices. Involving a non-zero real parameter \(\beta\) $\beta$ , the general F-temperature index \(T_{\beta }\) $T_{\beta }$ is a temperature index having strong efficacy. In this paper, we employ discrete optimization and regression analysis to find optimal value(s) of \(\beta\) $\beta$ for which the prediction potential of \(T_{\beta }\) $T_{\beta }$ and the total \(\pi\) $\pi$ -electron energy \(E_{\pi }\) $E_{\pi }$ of polycyclic hydrocarbons is the strongest. This, in turn, answers an open problem proposed by Hayat & Liu (2024). Applications of the optimal values for \(T_{\beta }\) $T_{\beta }$ are presented a two-parametric family of carbon nanocones in predicting their \(E_{\pi }\) $E_{\pi }$ with significantly higher accuracy.