Mathematical Properties of a Novel Graph-Theoretic Irregularity Index with Potential Applicability in QSPR Modeling

Abstract

Irregularity indices are graph-theoretic parameters designed to quantify the irregularity in a graph. In this paper, we study the practical applicability of irregularity indices in QSPR modeling of the physicochemical and quantum-theoretic properties of compounds. Our comparative testing shows that the recently introduced (Formula presented.) index has significant priority in applicability over other irregularity indices. In particular, we show that the correlation potential of the (Formula presented.) index with certain physicochemical and quantum-theoretic properties such as the enthalpy of formation, boiling point, and (Formula presented.) -electron energies is significant. Our QSPR modeling suggests that the regression models with the aforementioned characteristics such as strong curve fitting are, in fact, linear. Considering this the motivation, the (Formula presented.) index was studied further, and we provide analytically explicit expressions of the (Formula presented.) index for certain graph operations and compositions. We conclude the paper by reporting the conclusions, implications, limitations, and future scope of the current study.