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On computing some degree based topological indices for backbone DNA networks

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Abstract

Chemical graph theory is the field which deals with the combination of chemistry and graph theory. In this paper, we find the degree based first and second K Bbanhatti, first and second hyper K Banhatti, first and second multiplicative K banhatti, first and second multiplicative hyper K banhatti, Sombor, KG, modified KG, multiplicative KG, multiplicative modified KG, K Harmonic and multiplicative K Harmonic Banhatti, first Banhatti and reduced Banhatti Sombor, delta Banhatti Sombor indices for backbone DNA and subdivided backbone DNA networks. These topological descriptors are computed by direct method.

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References

  1. Wilson, R.J.: Introduction to graph theory. Pearson Education India (1979)

  2. Bonchev, D.: Chemical Graph Theory: Introduction and Fundamentals, vol. 1. CRC Press (1991)

  3. Balaban, A.T., Ivanciuc, O.: Historical development of topological indices. In: Topological Indices and Related Descriptors in QSAR and QSPAR, pp. 31–68. CRC Press (2000)

  4. Ma, Y., Dehmer, M., Künzi, U.M., Tripathi, S., Ghorbani, M., Tao, J., Emmert-Streib, F.: The usefulness of topological indices. Inf. Sci. 606, 143–151 (2022). https://doi.org/10.1016/j.ins.2022.05.038

    Article  Google Scholar 

  5. Ali, M.A., Sardar, M.S., Siddique, I., Alrowaili, D.: Vertex-based topological indices of double and strong double graph of dutch windmill graph. J. Chem. (2021). https://doi.org/10.1155/2021/7057412

    Article  Google Scholar 

  6. Bonchev, D.: Information Theoretic Indices for Characterization of Chemical Structures (No. 5). Research Studies Press, pp. 1–10 (1983)

  7. Xu, K., Liu, M., Gutman, I., Furtula, B.: A survey on graphs extremal with respect to distance-based topological indices. MATCH Commun. Math. Comput. Chem. (2014)

  8. Dehmer, M., Emmert-Streib, F., Shi, Y.: Interrelations of graph distance measures based on topological indices. PloS One 9(4), e94985 (2014). https://doi.org/10.1016/j.amc.2016.10.024

    Article  Google Scholar 

  9. Zhang, X., Wu, X., Akhter, S., Jamil, M.K., Liu, J.B., Farahani, M.R.: Edge-version atom-bond connectivity and geometric arithmetic indices of generalized bridge molecular graphs. Symmetry 10(12), 751–786 (2018)

    Article  MATH  Google Scholar 

  10. Zhang, X., Awais, H.M., Javaid, M., Siddiqui, M.K.: Multiplicative Zagreb indices of molecular graphs. J. Chem. 2019, 1–19 (2019)

    Article  Google Scholar 

  11. Zhang, **ujun, Rauf, Abdul, Ishtiaq, Muhammad, Siddiqui, Muhammad Kamran, Muhammad, Mehwish Hussain: On degree based topological properties of two carbon nanotubes. Polycycl. Aromat. Compd. 10, 22–35 (2020)

    Google Scholar 

  12. Zhang, X., Jiang, H., Liu, J.B., Shao, Z.: The cartesian product and join graphs on edge-version atom-bond connectivity and geometric arithmetic indices. Molecules 23(7), 1–17 (2018)

    Article  Google Scholar 

  13. Zhang, X., Naeem, M., Baig, A.Q., Zahid, M.A.: Study of hardness of superhard crystals by topological indices. J. Chem. 10, 7–20 (2021)

    Google Scholar 

  14. Zhang, X., Siddiqui, M.K., Javed, S., Sherin, L., Kausar, F., Muhammad, M.H.: Physical analysis of heat for formation and entropy of Ceria Oxide using topological indices. Comb. Chem. High Throughput Screen. 25(3), 441–450 (2022)

    Article  Google Scholar 

  15. Siddiqui, M.K., Imran, M., Ahmad, A.: On zagreb indices, zagreb polynomials of some nanostar dendrimers. Appl. Math. Comput. 280, 132–139 (2016)

    MathSciNet  MATH  Google Scholar 

  16. Siddiqui, M.K., Naeem, M., Rahman, N.A., Imran, M.: Computing topological indicesof certain networks. J. Optoelectron. Adv. Mater. 18(9–10), 884–892 (2016)

    Google Scholar 

  17. Koam, A.N.A., Ahmad, A., Azeem, M., Siddiqui, M.K.: Algebraic properties for molecular structure of magnesium iodide. CMES-Comput. Model. Eng. Sci. 135(2), 1131–1146 (2023)

    Google Scholar 

  18. Roberts, R.W., Crothers, D.M.: Stability and properties of double and triple helices: dramatic effects of RNA or DNA backbone composition. Science 258(5087), 1463–1466 (1992). https://doi.org/10.1126/science.1279808

    Article  Google Scholar 

  19. Chen, A., Zhang, F.: Wiener index and perfect matchings in random phenylene chains. MATCH. Commun. Math. Comput. Chem. 61, 623–630 (2009). https://doi.org/10.1155/2015/568926

    Article  MathSciNet  MATH  Google Scholar 

  20. Bian, H., Zhang, F.: Tree-like polyphenyl systems with extremal Wiener indices. Match 61(3), 631–641 (2009)

    MathSciNet  MATH  Google Scholar 

  21. Gutman, I.: Geometric approach to degree-based topological indices Sombor indices. MATCH Commun. Math. Comput. Chem. 86(1), 11–16 (2021). https://doi.org/10.46793/match.90-2.495L

  22. Zahid, R., Naz, K., Ahmad, S.: Expected values of molecular descriptors in random polyphenyl chains. Emerg. Sci. J. 6(1), 151–165 (2022). https://doi.org/10.28991/ESJ-2022-06-01-012

  23. Naz, K., Ahmad, S., Bashier, E.: On computing techniques for Sombor index of some graphs. Math. Probl. Eng. (2022). https://doi.org/10.1155/2022/1329653

    Article  Google Scholar 

  24. Liu, J.B., Gu, J.J., Wang, K.: The expected values for the Gutman index, Schultz index, and some Sombor indices of a random cyclooctane chain. Int. J. Quantum Chem. 123(3), e27022 (2023). https://doi.org/10.1002/qua.27022

    Article  Google Scholar 

  25. Kulli, V.R.: On K Banhatti indices of graphs. J. Comput. Math. Sci. 7(4), 213–218 (2016)

    Google Scholar 

  26. Kulli, V.R., On, K.: On K hyper-Banhatti indices and coindices of graphs. Int. Res. J. Pure Algebr. 6(5), 300–304 (2016)

    Google Scholar 

  27. Kulli, V.R.: First multiplicative K Banhatti index and coindex of graphs. Ann. Pure Appl. Math. 11(2), 79–82 (2016)

    Google Scholar 

  28. Kulli, V.R.: On banhatti-sombor indices. SSRG Int. J. Appl. Chem. 8(1), 21–25 (2021). https://doi.org/10.47191/ijmcr/v10i12.01

    Article  Google Scholar 

  29. Kulli, Veerabhadrappa R., Harish, Neelakantappa, Chaluvaraju, Basavaraju, Gutman, Ivan: Mathematical properties of KG Sombor index. Bull. Int. Math. Virtual Inst. 12(2), 379–386 (2022). https://doi.org/10.7251/BIMVI2202379K

    Article  MathSciNet  Google Scholar 

  30. Aftab, M.H., Rafaqat, M., Hussain, M., Zia, T.: On the computation of some topological descriptors to find closed formulas for certain chemical graphs. J. Chem. (2021). https://doi.org/10.1155/2021/5533619

    Article  Google Scholar 

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Funding

This research is supported by the (UPAR) grants of United Arab Emirates University (UAEU) via Grant No. UPAR- G00003739.

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Authors and Affiliations

  1. Department of Mathematics, Comsats University Islamabad, Lahore Campus, Lahore, Pakistan

    Kiran Naz, Sarfraz Ahmad, Muhammad Kamran Siddiqui & Hafiz Muhammad Bilal

  2. Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE

    Muhammad Imran

Authors
  1. Kiran Naz
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  2. Sarfraz Ahmad
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  3. Muhammad Kamran Siddiqui
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  4. Hafiz Muhammad Bilal
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  5. Muhammad Imran
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Correspondence to Muhammad Kamran Siddiqui.

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Naz, K., Ahmad, S., Siddiqui, M.K. et al. On computing some degree based topological indices for backbone DNA networks. J. Appl. Math. Comput. 69, 3189–3204 (2023). https://doi.org/10.1007/s12190-023-01879-3

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  • DOI: https://doi.org/10.1007/s12190-023-01879-3

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