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 IRA index has significant priority in applicability over other irregularity indices. In particular, we show that the correlation potential of the IRA index with certain physicochemical and quantum-theoretic properties such as the enthalpy of formation, boiling point, and π-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 IRA index was studied further, and we provide analytically explicit expressions of the IRA index for certain graph operations and compositions. We conclude the paper by reporting the conclusions, implications, limitations, and future scope of the current study.

Keywords

• irregularity index
• enthalpy of formation
• boiling point
• π-electronic energy
• benzenoid hydrocarbon
• QSPR model