Comparative analysis of temperature-based graphical indices for correlating the total π-electron energy of benzenoid hydrocarbons

Abstract

In a graph [Formula: see text], the temperature [Formula: see text] of a vertex [Formula: see text] is defined as [Formula: see text], where n is the order of G and [Formula: see text] is the valency/degree of x. A topological/graphical index [Formula: see text] is a map [Formula: see text], where ∑ (respectively, [Formula: see text]) is the set of simple connected graphs (respectively, real numbers). Graphical indices are employed in quantitative structure-property relationship (QSPR) modeling to predict physicochemical/thermodynamic/biological characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as [Formula: see text], where [Formula: see text] is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices named as the reduced reciprocal product-connectivity temperature ([Formula: see text]) index and the geometric-arithmetic temperature ([Formula: see text]) index. The predictive potential of these indices has been investigated by employing them in structure-property modeling of the total [Formula: see text]-electronic energy [Formula: see text] of benzenoid hydrocarbons. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data for [Formula: see text] is also publicly available. First, we employ a computer-based computational method to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of [Formula: see text] for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, linear. Our statistical analysis asserts that both [Formula: see text] and [Formula: see text] outperformed all the existing temperature indices for correlating [Formula: see text] for the BHs. The results suggest their further employability in QSPR modeling. Importantly, our research contributes toward countering proliferation of graphical indices.