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

Sakander Hayat, Amina Arif, Laiq Zada, Asad Khan () and Yubin Zhong ()
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Sakander Hayat: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Amina Arif: Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan
Laiq Zada: Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Swabi 23460, Pakistan
Asad Khan: School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
Yubin Zhong: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Mathematics, 2022, vol. 10, issue 22, 1-24

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 I R A index has significant priority in applicability over other irregularity indices. In particular, we show that the correlation potential of the I R A 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 I R A index was studied further, and we provide analytically explicit expressions of the I R A 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; ?-electronic energy; benzenoid hydrocarbon; QSPR model; transformation graph; derived graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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