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Novel neighbourhood redefined first and second Zagreb indices on carborundum structures

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Abstract

Graph theory offers experts with a useful tool called the topological index which analyses the characteristics of chemical compounds. Motivated by the recent work of redefined Zagreb indices (\(ReZG_{1}\), \(ReZG_{2}\), \( ReZG_{3}\)), novel topological indices such as Neighbourhood redefined first and second Zagreb indices (\(NReZ_{1}\), \(NReZ_{2}\)) are proposed and computed for a molecular graph G of two carborundum structures. The correlation coefficient of \(NReZ_{1}\), \(NReZ_{2}\) with ten properties of octane isomers are determined, of which entropy and acentric factor showed a good correlation. Also, the lower and upper bounds of redefined Zagreb indices are determined using classic results, Pólya–Szegö and Cauchy–Schwarz inequalities for simple graphs and trees.

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Authors and Affiliations

  1. Department of Mathematics, Jain Institute of Technology, Davanagere, 577003, India

    M. C. Shanmukha

  2. Affiliated to Visvesvaraya Technological University, Belagavi, Karnataka, India

    M. C. Shanmukha, N. S. Basavarajappa & K. C. Shilpa

  3. Department of Mathematics, Bapuji Institute of Engineering and Technology, Davanagere, 577004, India

    N. S. Basavarajappa

  4. Department of Mathematics, Alliance College of Engineering and Design, Alliance University, Anekal-Chandapura Road, Bangalore, Karnataka, India

    A. Usha

  5. Department of Computer Science and Engineering, Bapuji Institute of Engineering and Technology, Davanagere, 577004, India

    K. C. Shilpa

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  1. M. C. Shanmukha
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  2. N. S. Basavarajappa
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  3. A. Usha
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  4. K. C. Shilpa
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Correspondence to M. C. Shanmukha.

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Shanmukha, M.C., Basavarajappa, N.S., Usha, A. et al. Novel neighbourhood redefined first and second Zagreb indices on carborundum structures. J. Appl. Math. Comput. 66, 263–276 (2021). https://doi.org/10.1007/s12190-020-01435-3

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  • DOI: https://doi.org/10.1007/s12190-020-01435-3

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