Optimizing structure-property models of three general graphical indices for thermodynamic properties of benzenoid hydrocarbons

Cheminformatics is an interdisciplinary field that combines principles of chemistry, computer science, and information technology to process, store, analyze, and interpret chemical data. One area of cheminformatics is quantitative structure–property relationship (QSPR) modeling which is a computational approach that correlates the structural attributes of chemical compounds with their physical, chemical, or biological properties to predict the behavior and characteristics of new or untested compounds. Structure descriptors deliver contemporary mathematical tools required for QSPR modeling. One of a significant class of such descriptors is graph-based descriptors known as graphical descriptors. A degree-based graphical descriptor/invariant of a $\upsilon$-vertex graph $\Omega =(V_{\Omega },E_{\Omega })$ has a general structure $G{D}_d={\sum }_{ij\in E_{\Omega }}\pi \left({\mathrm{deg}}_{x_i},{\mathrm{deg}}_{x_j}\right)$, where $\pi$ is bivariate symmetric map, and ${\mathrm{deg}}_{x_i}$ is the degree of vertex $x_i\in V_{\Omega }$. For $\alpha \in R\setminus \left\{0\right\}$, if $\pi ={({\mathrm{deg}}_{x_i}\times {\mathrm{deg}}_{x_j})}^{\alpha }$ (resp. $\pi ={({\mathrm{deg}}_{x_i}+{\mathrm{deg}}_{x_j})}^{\alpha }$, then $G{D}_d$ is called the general product-connectivity $P{C}_{\alpha }$ (resp. sum-connectivity $S{C}_{\alpha }$) index of $\Omega$. Moreover, the general Sombor index $S{O}_{\alpha }$ has the structure $\pi ={({\mathrm{deg}}_{x_i}^2\times {\mathrm{deg}}_{x_j}^2)}^{\alpha }$. By choosing the heat capacity $\Delta H$ and the entropy $E$ as representatives of thermodynamic properties, we in this paper find optimal value(s) of $\alpha$ which deliver the strongest potential of the predictors $G{D}_d\in \{P{C}_{\alpha },S{C}_{\alpha },S{O}_{\alpha }\}$ for predicting $\Delta H$ and $E$ of benzenoid hydrocarbons. In order to achieve this, we employ tools such as discrete optimization and multivariate regression analysis. This, in turn, study completely solves two open problems proposed in the literature.