Chemical applicability of $π$-Sombor index

The Sombor index ($SO$) and the modified Sombor index (${}^m SO$) are two closely related vertex-degree-based graph invariants. Both were introduced in the early 2020s and have found diverse applications in chemical, physicochemical, and network-theoretical studies. In 2023, the $\pi$-Sombor index was introduced as the product $SO \cdot {}^m SO$, with an initial focus on its fundamental mathematical properties. However, its potential chemical applicability has remained unexplored. In the present work, we address this gap by employing regression models to analyze the $\pi$-Sombor index in 22 benzenoid hydrocarbons. This study investigates the chemical significance of the $\pi$-Sombor index through curvilinear regression analysis against the physicochemical properties of these hydrocarbons.