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

Author

Listed:
  • Sakander Hayat

    (School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Sakander Hayat & Amina Arif & Laiq Zada & Asad Khan & Yubin Zhong, 2022. "Mathematical Properties of a Novel Graph-Theoretic Irregularity Index with Potential Applicability in QSPR Modeling," Mathematics, MDPI, vol. 10(22), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4377-:d:978874
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    References listed on IDEAS

    as
    1. Chen, Xiaodan & Hou, Yaoping & Lin, Fenggen, 2018. "Some new spectral bounds for graph irregularity," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 331-340.
    2. Abdo, Hosam & Dimitrov, Darko & Gutman, Ivan, 2019. "Graph irregularity and its measures," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 317-324.
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