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.

On the Entire Harmonic Index and Entire Harmonic Polynomial of Graphs

“…So, we examine the significance of the entire Harmonic index for predicting for key properties like the total π-electronic energy (E π ), enthalpy of formation (∆ o f ), and boiling points (Bp) of 16 lower benzenoid hydrocarbons, see Figure 1. The experimental data of the total π-electronic energy (E π ), enthalpy of formation (∆ o f ), and boiling points (Bp) are taken from NIST databases [35] and retrieved from [36]. Analysis of the data in Table 1 highlights the emergence of the entire Harmonic index as a promising descriptor for diverse physicochemical properties.…”