The Exploring Kevlar's Chemical Structure through Advanced Topological Co-Indices
Exploring Kevlar's Chemical Structure
DOI:
https://doi.org/10.63960/sijmds-2025-2359Keywords:
Topological co-indices, physical parameters, Zagreb type co-indice, Geometric Randic topological co-indicesAbstract
Unlocking the secrets of molecular structures has become a paramount pursuit in the
realm of scientific inquiry, where the marriage of mathematical models and physical properties
plays a pivotal role. Topological co-indices, as mathematical constructs, serve as potent tools
to scrutinize the intricate relationship between chemical structures and their properties. By
harnessing the power of molecular graphs, where edges represent bonds and points symbolize
atoms, these co-indices provide numerical insights into diverse chemical structures.
In this study, we delve into the fascinating world of topological co-indices by employing
the iconic Kevlar’s chemical structure as our focal point. Unlike conventional lab tests, our
approach offers a time-efficient alternative, enabling frequent usage without compromising
accuracy. The investigation encompasses the derivation and analysis of several topological
co-indices tailored to the unique attributes of Kevlar. Furthermore, this research introduces
graphical representations that vividly illustrate the comparative landscape of estimated topo-
logical indices associated with Kevlar’s chemical structure. These visuals serve as a powerful
tool for both experts and enthusiasts, enhancing the accessibility and comprehensibility of
our findings. Join us on this captivating journey as we unravel the mathematical intricacies
intertwined with the physical essence of Kevlar’s molecular architecture, shedding light on
its distinctive properties through the lens of topological co-indices.
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References
Shao, Z., Javed, M. S., & Farahani, M. R. (2019). Degree-based graph invariants for the molecular graph of Bismuth Tri-Iodide. Engineering Applications of Science Research, 2, 1–11. https://doi.org/10.1016/j.jksus.2020.01.013
Keith, J. A., Vassilev-Galindo, V., Cheng, B., Chmiela, S., Gastegger, M., Müller, K.-R., & Tkatchenko, A. (2021). Combining machine learning and computational chemistry for predictive insights into chemical systems. Chemical Reviews, 121, 9816–9872. https://doi.org/10.1021/acs.chemrev.0c01212
Cova, T. F., & Pais, A. A. (2019). Deep learning for deep chemistry: Optimizing the prediction of chemical patterns. Frontiers in Chemistry, 7, 809. https://doi.org/10.3389/fchem.2019.00809
Ayers, P. L., et al. (2015). Six questions on topology in theoretical chemistry. Computational and Theoretical Chemistry, 1053, 2–16. https://doi.org/10.1016/j.comptc.2014.09.008
Kwun, Y. C., et al. (2017). M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori. Scientific Reports, 7, 8756. https://doi.org/10.1038/s41598-017-09321-3
Speck-Planche, A. (2018). Combining ensemble learning with a fragment-based topological approach to generate new molecular diversity in drug discovery: In silico design of Hsp90 inhibitors. ACS Omega, 3, 14704–14716. https://doi.org/10.1021/acsomega.8b02142
Xavier, D. A., et al. (2023). Comparative study of molecular descriptors of pent-heptagonal nanostructures using neighborhood M-polynomial approach. Molecules, 28, 2518. https://doi.org/10.3390/molecules28062518
Basavanagoud, B., et al. (2017). Computing first Zagreb index and F-index of new C-products of graphs. Applied Mathematics & Nonlinear Sciences, 2, 285–298. https://doi.org/10.21042/AMNS.2017.2.00023
Ali, F., et al. (2022). On the topological indices of commuting graphs for finite non-Abelian groups. Symmetry, 14, 1266. https://doi.org/10.3390/sym14061266
Wiener, H. (1947). Structural determination of paraffin boiling points. Journal of the American Chemical Society, 69, 17–20. https://doi.org/10.1021/ja01193a005
Gutman, I., Milovanović, E., & Milovanović, I. (2018). Beyond the Zagreb indices. AKCE International Journal of Graphs and Combinatorics. https://doi.org/10.1016/j.akcej.2018.09.002
Randić, M. (1975). Characterization of molecular branching. Journal of the American Chemical Society, 97, 6609–6615. https://doi.org/10.1021/ja00856a001
Sahin, B., & Ediz, S. (2018). On ev-degree and ve-degree topological indices. Iranian Journal of Mathematical Chemistry, 9, 263–277. https://doi.org/10.22052/IJMC.2018.142268.1376
Consonni, V., & Todeschini, R. (2010). Molecular descriptors. In Recent advances in QSAR studies: Methods and applications (pp. 29–102). https://doi.org/10.1007/978-90-481-3885-0_2
Koam, A. N., Ahmad, A., & Nadeem, M. F. (2021). Comparative study of valency-based topological descriptor for hexagon star network. Computer Systems Science and Engineering, 36, 293–306. https://doi.org/10.32604/csse.2021.014477
Nadeem, M. F., et al. (2021). Topological aspects of metal-organic structure with the help of underlying networks. Arabian Journal of Chemistry, 14, 103157. https://doi.org/10.1016/j.arabjc.2021.103157
Ahmad, Z., Mufti, Z. S., Nadeem, M. F., Shaker, H., & Siddiqui, H. M. A. (2021). Theoretical study of energy, inertia and nullity of phenylene and anthracene. Open Chemistry, 19, 541–547. https://doi.org/10.1515/chem-2021-0052
Sun, C., et al. (2022). On neighborhood degree-based topological analysis of polyphenylene network. Mathematical Problems in Engineering, 2022, Article ID 7090518. https://doi.org/10.1155/2022/7090518
Zhao, D., et al. (2021). Computation and analysis of topological co-indices for metal-organic compounds. Current Organic Synthesis, 18, 750–760. https://doi.org/10.2174/1570179417666210225123003
Hayat, S., Wang, S., & Liu, J.-B. (2018). Valency-based topological descriptors of chemical networks and their applications. Applied Mathematical Modelling, 60, 164–178. https://doi.org/10.1016/j.apm.2018.03.017
Huang, R., Muhammad, M. H., Siddiqui, M. K., Nasir, M., & Cancan, M. (2022). On degree based topological co-indices of graphite carbon nitride. Polycyclic Aromatic Compounds, 42, 5616–5625. https://doi.org/10.1080/10406638.2020.1816455
Gao, W., Husin, M. N., Farahani, M. R., & Imran, M. (2016). On the edges version of atom-bond connectivity index of nanotubes. Journal of Computational and Theoretical Nanoscience, 13, 6733–6740. https://doi.org/10.1166/jctn.2016.5626
Gao, W., Jamil, M. K., Nazeer, W., & Amin, M. (2017). Degree-based multiplicative atom-bond connectivity index of nanostructures. IAENG International Journal of Applied Mathematics, 47(1), 1–10. http://www.iaeng.org/IJAM/issues_v47/issue_1/IJAM_47_1_01.pdf
Mormann, W., Hellwich, K.-H., Chen, J., & Wilks, E. S. (2017). Preferred names of constitutional units for use in structure-based names of polymers (IUPAC Recommendations 2016). Pure and Applied Chemistry, 89, 1695–1736. https://doi.org/10.1515/pac-2016-0402
Khalifeh, M., Yousefi-Azari, H., & Ashrafi, A. R. (2009). The first and second Zagreb indices of some graph operations. Discrete Applied Mathematics, 157, 804–811. https://doi.org/10.1016/j.dam.2008.08.002
Yang, J., et al. (2022). Topological co-indices of hydroxyethyl starch conjugated with hydroxychloroquine used for COVID-19 treatment. Polycyclic Aromatic Compounds, 42, 7130–7142. https://doi.org/10.1080/10406638.2020.1850931
Ghorbani, M., & Azimi, N. (2012). Note on multiple Zagreb indices. Iranian Journal of Mathematical Chemistry, 3, 137–143. https://ijmc.kashanu.ac.ir/article_9224.html
Milovanović, I., Matejić, M., Milovanović, E., & Khoeilar, R. (2021). A note on the first Zagreb index and coindex of graphs. Communications in Combinatorics and Optimization, 6, 41–51. https://doi.org/10.22052/CCO.2021.246158.1045
Khalid, A., et al. (2022). Topological co-indices of molecular structure of porphyrazine network. Polycyclic Aromatic Compounds, 1–11. https://doi.org/10.1080/10406638.2022.2052724
Liu, J. B., Wang, S., Wang, C., & Hayat, S. (2017). Further results on computation of topological indices of certain networks. IET Control Theory & Applications, 11, 2065–2071. https://doi.org/10.1049/iet-cta.2016.1083
Fath-Tabar, G. H., Vaez-Zadeh, B., Ashrafi, A. R., & Graovac, A. (2011). Some inequalities for the atom-bond connectivity index of graph operations. Discrete Applied Mathematics, 159, 1323–1330. https://doi.org/10.1016/j.dam.2011.03.013
Das, K. C. (2010). Atom-bond connectivity index of graphs. Discrete Applied Mathematics, 158, 1181–1188. https://doi.org/10.1016/j.dam.2009.12.002
Berhe, M., & Wang, C. (2019). Computation of certain topological coindices of graphene sheet and nanotubes and nanotorus. Journal of Computational and Theoretical Nanoscience, 4, 455–468. https://doi.org/10.1166/jctn.2019.8046
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Copyright (c) 2025 Umar Farooq, Faryal Chaudhary, Wasim Abbas

This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2025-07-30
Published 2025-09-07