Analysis of degree-based topological indices through M-polynomial of metal trihalides
*Zahid RazaCorresponding authorzraza@sharjah.ac.aeDepartment of MathematicsCollege of SciencesUniversity of SharjahSharjah, P. O. Box. 27272, UAEView full profile → , Juan LG Guiraojuan.garcia@upct.esAffiliation 1Departamento de Matematica Aplicada y EstadisticaUniversidad Politecnica de CartagenaHospital de MarinaMurcia, 30203, SpainAffiliation 2Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah, P. O. Box 80203, 21589, Saudi ArabiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Nov 2022
- Published Online:
- 28 Jul 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1872
- Pages:
- 15–33
Abstract
Keywords
Subject Classifications
References
[1] S. C. Basak, “Use of graph invariants in quantitative structure-activity relationship studies,” Croatica Chemica Acta, vol. 89, no. 4, pp. 1–6, 2016.
[2] O. Ivanciuc, “Chemical graphs, molecular matrices and topological indices in chemoinformatics and quantitative structure-activity relationships,” Current Computer-Aided Drug Design, vol. 9, no. 2, pp. 153–163, 2013.
[3] I. Gutman and N. Trinajstić, “Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons,” Chemical Physics Letters, vol. 17, no. 4, pp. 535–538, 1972.
[4] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, “The Zagreb indices 30 years after,” Croatica Chemica Acta, vol. 76, pp. 113–124, 2003.
[5] Y. M. Chu, M. Imran, A. Q. Baig, S. Akhter, and M. K. Siddiqui, “On M-polynomial-based topological descriptors of chemical crystal structures and their applications,” European Physical Journal Plus, vol. 135, p. 874, 2020. doi: 10.1140/epjp/s13360-020-00893-9.
[6] E. Deutsch and S. Klavžar, “M-polynomial and degree-based topological indices,” Iranian Journal of Mathematical Chemistry, vol. 6, pp. 93–102, 2015.
[7] E. Deutsch and S. Klavžar, “M-polynomial revisited: Bethe cacti and an extension of Gutman’s approach,” Journal of Applied Mathematics and Computing, vol. 60, pp. 253–264, 2019.
[8] Z. Raza, “The harmonic and second Zagreb indices in random polyphenyl and spiro chains,” Polycyclic Aromatic Compounds, vol. 42, no. 3, pp. 671–680, 2022. doi: 10.1080/10406638.2020.1749089.
[9] M. Munir, W. Nazeer, S. Rafque, and S. M. Kang, “M-polynomial and degree-based topological indices of polyhex nanotubes,” Symmetry, vol. 8, p. 149, 2016, doi: 10.3390/sym8120149.
[10] H. Yang, A. Q. Baig, W. Khalid, M. R. Farahani, and X. Zhang, “M-polynomial and topological indices of benzene ring embedded in P-type surface network,” Journal of Chemistry, Article ID 7297253, 2019, doi: 10.1155/2019/7297253.
[11] Z. Raza and M. E. Sukaiti, “M-polynomial and degree-based topological indices of some nanostructures,” Symmetry, vol. 12, p. 831, 2020, doi: 10.3390/sym12050831.
[12] J. B. Liu, Z. Raza, and M. Javaid, “Zagreb connection numbers for cellular neural networks,” Discrete Dynamics in Nature and Society, vol. 2020, Article ID 8038304, 8 pages, 2020, doi: 10.1155/2020/8038304.
[13] A. Eftekhari and H. Garcia, “Materials Today Chemistry,” Materials Today, vol. 4, pp. 117–132, 2017.
[14] C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science, vol. 321, no. 5887, pp. 385–388, 2008.
[15] P. Miric, M. Audiffred, and T. Heine, “An atlas of two-dimensional materials,” Chemical Society Reviews, vol. 43, no. 18, pp. 6537–6554, 2014.
[16] M. Xu, T. Liang, M. Shi, and H. Chen, “Graphene-like two-dimensional materials,” Chemical Reviews, vol. 113, no. 5, pp. 3766–3798, 2013.
[17] L. P. Feng, J. Su, and Z. T. Liu, “Effect of vacancies in monolayer MoS 2 on electronic properties of MoMoS 2 contacts,” RSC Advances, vol. 5, no. 26, pp. 20538–20544, 2015.
[18] A. Ali, Z. Raza, and A. A. Bhatti, “Bond incident degree (BID) indices for some nanostructures,” Optoelectronics and Advanced Materials – Rapid Communications, vol. 10, no. 1–2, pp. 108–112, 2016.
[19] A. Ali, A. A. Bhatti, and Z. Raza, “Further inequalities between vertex-degree-based topological indices,” International Journal of Applied and Computational Mathematics, vol. 3, no. 3, pp. 1921–1930, 2017, doi: 10.1007/s40819-016-0213-4.
[20] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, Weinheim, 2009.
[21] K. Balasubramanian, “Mathematical and computational techniques for drug discovery: promises and developments,” Current Topics in Medicinal Chemistry, vol. 18, no. 32, pp. 2774–2799, 2018.
[22] K. Balasubramanian and S. P. Gupta, “Quantum molecular dynamics, topological, group theoretical and graph theoretical studies of protein-protein interactions,” Current Topics in Medicinal Chemistry, vol. 19, no. 6, pp. 426–443, 2019.
[23] S. C. Basak, D. Mills, and M. M. Mumtaz, “Quantitative structure-activity relationship (QSAR) study of dermal absorption using theoretical molecular descriptors,” SAR and QSAR in Environmental Research, vol. 18, no. 1–2, pp. 45–55, 2007.
[24] M. Arockiaraj, J. Clement, and K. Balasubramanian, “Analytical expressions for topological properties of polycyclic benzenoid networks,” Journal of Chemometrics, vol. 30, no. 11, pp. 682–697, 2016.
[25] M. Arockiaraj, S. R. J. Kavitha, S. Mushtaq, and K. Balasubramanian, “Relativistic topological molecular descriptors of metal trihalides,” Journal of Molecular Structure, vol. 1217, p. 128368, 2020.
[26] M. A. McGuire, “Crystal and magnetic structures in layered, transition metal dihalides and trihalides,” Crystals, vol. 7, no. 5, pp. 121–131, 2017.
[27] A. Ali, A. A. Bhatti, and Z. Raza, “The augmented Zagreb index, vertex connectivity and matching number of graphs,” Bulletin of the Iranian Mathematical Society, vol. 42, no. 2, pp. 417–425, 2016.
[28] M. N. J. Baig, C. Y. Jung, N. Ahmad, and S. M. Kang, “On the M-polynomials and degree-based topological indices of an important class of graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 22, no. 7, pp. 1281–1288, 2019, doi: 10.1080/09720529.2019.1691327.
[29] D. Afzal, S. Ali, F. Afzal, M. Cancan, S. Ediz, and M. R. Farahani, “A study of newly defined degree-based topological indices via M-polynomial of Jahangir graph,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 2, pp. 427–438, 2021, doi: 10.1080/09720529.2021.1882159.
[30] F. Chaudhry, M. N. Husin, F. Afzal, D. Afzal, M. Ehsan, M. Cancan, and M. R. Farahani, “M-polynomials and degree-based topological indices of tadpole graph,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 7, pp. 2059–2072, 2021, doi: 10.1080/09720529.2021.1984561.




