A Comparative Study: Domination Parameters and Physico-Chemical Properties of Benzenoid Hydrocarbons

In graph theory, a graph is a mathematical structure that consists of a set of vertices and a set of edges connecting those pairs of vertices. Let $G=(V,E)$ be a graph, a dominating set for G is a subset $D\subseteq V$ of vertices such that every vertex in $V\setminus D$ has at least one neighbor in D. The domination number of G, denoted by $\gamma \left(G\right),$ is the minimum cardinality of a dominating set in G. Recently, Khan (2023) performed a comparative study of seven important domination parameters with the $\pi$-electronic energy of benzenoid hydrocarbons, with a new theoretical approach. Physico-chemical properties are crucial for understanding the physical and chemical behavior of a molecule. In this paper, we perform a comparative study of those seven domination parameters with the physico-chemical properties of benzenoid hydrocarbons. We find the values of those domination parameters for the 22 lower benzenoid hydrocarbons and follow the statistical approach described by Khan (2023). The two physico-chemical properties to be chosen are the normal boiling point $T_b,$ a representative for intermolecular and van-der-Waals type interactions, whereas, the standard enthalpy/heat of formation $\Delta H_f^o$ is referred to represent the thermal properties of a molecular graph. This study further enhances that the performance of paired domination number is exceptional among all other parameters and highly correlated with both of the physico-chemical properties. Its correlation coefficient is 0.9981 (respectively, 0.9726) with $T_b$ (respectively, $\Delta H_f^o$). The outstanding correlation coefficient of paired domination number ensures further usage in quantitative structure-property relationship (QSPR) models.