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A novel approach to determine the Sombor-type indices via M-polynomial

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Abstract

Topological indices can be interpreted as the mathematical characterizations of a molecular compound and are significantly employed to forecast its physical, chemical and biological information. Computation of topological indices of a graph through its associated graph polynomial is a modern and optimal approach. One such method is to determine the degree-based topological indices of a graph using its M-polynomial. Among the class of degree-based topological indices, the Sombor indices are one of the most investigated indices in recent times. In this article, the M-polynomial-based derivation formulas are derived to compute the different Sombor-type indices, namely the Sombor index, modified Sombor index, first and second Banhatti–Sombor indices, and their reduced form of the Sombor indices. Furthermore, our proposed derivation formulas are applied to compute the Sombor-type indices of the jagged-rectangle benzenoid system \(B_{m,n}\). Additionally, the comparison among the Sombor-type indices of \(B_{m,n}\) is presented through numerical and graphical representations.

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Notes

  1. Quantitative Structure–Property Relationship.

  2. Quantitative Structure-Activity Relationship.

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Acknowledgements

The authors are grateful to the reviewer(s) for the thorough review of our manuscript. The valuable comments and suggestions have helped us to improve the quality of the article. Moreover, The first author (Virendra Kumar) is grateful to the UNIVERSITY GRANTS COMMISSION, Ministry of Human Resource Development, India for awarding the Senior Research Fellowship (SRF) with reference to UGC-Ref. No.: 1127/(CSIR-UGC NET JUNE 2019) dated 11-December-2019. The second author (Dr. Shibsankar Das) is obliged to the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India for financially supporting this work through the SERB’s research project sanction order number: EEQ/2022/000313, dated 20-January-2023.

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  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, 221005, India

    Virendra Kumar & Shibsankar Das

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  1. Virendra Kumar
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Kumar, V., Das, S. A novel approach to determine the Sombor-type indices via M-polynomial. J. Appl. Math. Comput. 71, 983–1007 (2025). https://doi.org/10.1007/s12190-024-02272-4

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  • DOI: https://doi.org/10.1007/s12190-024-02272-4

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