Original Research Article

Article volume = 2023 and issue = 2

Pages: 177–187

Article publication Date: November 28, 2023

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# Expected values of various degree-based graph invariants of Azythromycin

#### M.C. Shanmukha(a), A. Usha(b), and G.S. Pallavi(c)

(a) Department of Mathematics, PES Institute of Technology and Management, Shivamogga-577204, India.

(b) Department of Mathematics, Alliance School of Applied Mathematics, Bangalore-562106, India.

(c) Department of Mathematics, Bapuji Institute of Engineering & Technology, Davanagere-577004, India.

##### Abstract:

The greatest innovation of the 20th century is the launch of antibiotics into the clinical use. It helps in treating infectious diseases caused by bacteria and in addition to this, it is used in the cancer treatment, organ transplant and open-heart surgery. This work focusses on a miracle antibiotic, Azithromycin which is used in several diseases caused by bacteria. The detailed study on this compound is discussed in the forthcoming sections. This article pinpoints on computing various degree-based topological indices for Azithromycin followed by the numerical representation of the considered indices in tabulated form for better understanding.

##### Keywords:

Chemical graph theory, topological indices, Azithromycin.

##### References:

- [1] Bakheit, A. H., Al-Hadiya, B. M., & Abd-Elgalil, A. A. (2014). Azithromycin. Profiles of drug substances, excipients and related methodology, 39, 1-40. 1
- [2] El-Rjoob, A. W., Al-Mustafa, J., Taha, Z., & Abous, M. (2008). Spectroscopic and conductometric investigation of the interaction of azithromycin with iron (II) ion. Jordan Journal of Chemistry (JJC), 3(2), 199-209. 1
- [3] Echeverría-Esnal, D., Martin-Ontiyuelo, C., Navarrete-Rouco, M. E., De-Antonio Cuscó, M., Ferrández, O., Horcajada, J. P., & Grau, S. (2021). Azithromycin in the treatment of COVID-19: a review. Expert review of anti-infective therapy, 19(2), 147-163. 1
- [4] James M. McCarty (1996). Azithromycin (Zithromax(R)). Infectious Diseases in Obstetrics and Gynecology, 4:215-220 (1996). 1
- [5] Matthew I Hutchings, Andrew W Truman and Barrie Wilkinson (2019). Antibiotics: past, present and future. Elsevier, https://doi.org/10.1016/j.mib.2019.10.008, 72-80. 1
- [6] Parnham, M. J., Haber, V. E., Giamarellos-Bourboulis, E. J., Perletti, G., Verleden, G. M., & Vos, R. (2014). Azithromycin: mechanisms of action and their relevance for clinical applications. Pharmacology & therapeutics, 143(2), 225-245. 1
- [7] Oliver, M. E., & Hinks, T. S. (2021). Azithromycin in viral infections. Reviews in medical virology, 31(2), e2163. 1
- [8] Harishchandra S. Ramane, Raju B. Jummannaver, Note on forgotten topological index of chemical structure in drugs, Applied Mathematics and Nonlinear Sciences 1(2016), 369–374. 1
- [9] A. Yurtas, M. Togan, V. Lokesha et al. Inverse problem for Zagreb indices. J Math Chem 57(2019), 609–615. Doi.org/10.1007/s10910-018-0970-x. 1
- [10] R. Todeschini, and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000. 1
- [11] W. Gao, M.R. Farahani, M.K. Jamil, and M.K. Siddiqui, The Redefined First, Second and Third Zagreb Indices of Titania Nanotubes TiO2[m; n], The Open Biotechnology Journal, 10(2016), 272-277. 1
- [12] Lokesha Veerebradiah, Suvarna, Cevik Ahmet and Cangul Ismail naci. (2021). V L Reciprocal Status Index and Co-Index of Graphs. Journal of Mathematics. 2021. 1-10. 10.1155/2021/5529080. 1
- [13] M. Randic, Quantitative Structure-Property Relationship: Boiling Points and Planar Benzenoids, New. J. Chem., 20(1996), 1001-1009. 1
- [14] M. Randic, Novel molecular descriptor for structure-property studies, Chemical Physics Letters, 211(1993), 478–483. 1
- [15] H. Wiener, Structural determination of paraffin boiling points, Journal of the American Chemical Society, 69(1947),17–20. 1
- [16] Jian-Feng Zhong, Abdul Rauf, Muhammad Naeem, Jafer Rahman, Adnan Aslam, Quantitative structure-property relationships (QSPR) of valency based topological indices with Covid-19 drugs and application, Arabian Journal of Chemistry, 14(2021),1-16. 1
- [17] Shanmukha, M. C., Usha, A., Praveen, B. M., & Douhadji, A. (2022). Degree-based molecular descriptors and QSPR analysis of breast cancer drugs. Journal of Mathematics, 2022, 1-13. 1
- [18] Zhang, X., Reddy, H. G., Usha, A., Shanmukha, M. C., Reza Farahani, M., & Alaeiyan, M. (2022). A study on anti-malaria drugs using degree-based topological indices through QSPR analysis. 1
- [19] Shanmukha, M. C., Ismail, R., Gowtham, K. J., Usha, A., Azeem, M., & Al-Sabri, E. H. A. (2023). Chemical applicability and computation of K-Banhatti indices for benzenoid hydrocarbons and triazine-based covalent organic frameworks. Scientific Reports, 13(1), 17743. 1
- [20] E. Estrada E, E. Uriarte, Recent advances on the role of topological indices in drug discovery research, Curr Med Chem., 8(13)(2001), 1573-88. Doi: 10.2174/0929867013371923. 1
- [21] Ö.Ç. Havare, Topological indices and QSPR modeling of some novel drugs used in the cancer treatment, International Journal of Quantum Chemistry, 2021, 1-23. Doi:10.1002/qua.26813. 1
- [22] F. Harary, Graph Theory, Addison-Wesely, Reading Mass, 1969. 1
- [23] V.R. Kulli, College Graph Theory, Vishwa Int. Publ., Gulbarga, India, 2012. 1
- [24] N. Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, FL. 1992. 1
- [25] I. Gutman, and N. Trinajstic, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17(1972), 535-538. 1
- [26] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986. 1
- [27] M. Randic, On Characterization of Molecular Branching, J. Am. Chem. Soc., 97(1975), 6609-6615. 1
- [28] B. Bollobas, P. Erdos, Graphs of extremal weights. Ars Combinatoria, 50(1998), 225-233. 1
- [29] Fajtlowicz, S. (1988). On conjectures of Graffiti. In Annals of Discrete Mathematics, Vol. 38, pp. 113-118. 1
- [30] Zhou, B., & Trinajstić, N. (2009). On a novel connectivity index. Journal of mathematical chemistry, 46, 1252-1270. 1
- [31] Weidong Zhao, M.C. Shanmukha, A. Usha, Mohammad Reza Farahani and K.C. Shilpa, Computing SS Index of Certain Dendrimers, Journal of Mathematics, vol. 2021, Article ID 7483508, 14 pages, 2021. https://doi.org/10.1155/2021/7483508. 1
- [32] B. Furtula and I. Gutman, A Forgotten Topological Index, Journal of Mathematical Chemistry, 53(2015), 1184-1190. 1
- [33] E. Estrada, L. Torres, L. Rodracuteiguez, I. Gutman, An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes. Indian J. Chem., 37A(1998), 849-855. 1
- [34] D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem., 46(2009), 1369-1376, https://doi.org/10.1007/s10910-009-9520-x. 1
- [35] A. Usha, M.C. Shanmukha, K.N. Anil Kumar and K.C. Shilpa, Comparision of novel index with geometric-arithmetic and sum-connectivity indices, 11(2021), 5344-5360. 1
- [36] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem., 86 (2021) 11-16. 1
- [37] Ghorbani, M., & Hosseinzadeh, M. A. (2010). Computing ABC4 index of nanostar dendrimers. Optoelectronics and Advanced Materials-Rapid Communications, 4(September 2010), 1419-1422. 1
- [38] Graovac, A., Ghorbani, M., & Hosseinzadeh, M. A. (2011). Computing fifth geometric-arithmetic index for nanostar dendrimers. Journal of Discrete Mathematics and Its Applications, 1(1-2), 33-42. 1

##### Cite this article as:

- M.C. Shanmukha, A. Usha, and G.S. Pallavi, Expected values of various degree-based graph invariants of Azythromycin, Communications in Combinatorics, Cryptography & Computer Science, 2023(2), PP.177–187, 2023
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