The Exploring Kevlar's Chemical Structure through Advanced Topological Co-Indices

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Authors

  • Umar Farooq Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan Author
  • Faryal Chaudhary Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan Author
  • Wasim Abbas Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan Author

Keywords:

Topological co-indices, physical parameters, Zagreb type co-indice, Geometric Randic topological co-indices

Abstract

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 topological 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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Author Biographies

  • Umar Farooq, Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Umar Farooq pursing a PhD in Mathematics from The University of Lahore. His research focuses on mathematical chemistry and network optimization, specifically metric, edge metric, and fault-tolerant metric dimensions in molecular graphs. He applies theoretical graph invariants to chemistry and artificial intelligence, co-authoring papers in international scientific journals.

    Competing Interests:

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  • Faryal Chaudhary, Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Dr. Faryal Chaudhry is an Associate Professor of Mathematics and Statistics at The University of Lahore, holding a PhD in Mathematics from the Abdus Salam School of Mathematical Sciences (2016). Her expertise covers combinatorial algebra, graph theory, combinatorics, and fuzzy algebra. She has published extensively in international journals on mathematical modeling and topological indices.

    Competing Interests:

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  • Wasim Abbas, Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Wasim Abbas pursuing his PhD in Mathematics from The University of Lahore, alongside an MSc from Government College University, Faisalabad. Specializing in applied mathematics and network optimization, his research explores graph dimensions and topological properties of chemical networks.

    Competing Interests:

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Published

2025-09-07

Data Availability Statement

The data available at the request of the author.

Supporting Agencies

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Competing Interests

  • Umar Farooq:

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  • Faryal Chaudhary:

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  • Wasim Abbas:

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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How to Cite

Farooq, U., Chaudhary, F., & Abbas, W. (2025). The Exploring Kevlar’s Chemical Structure through Advanced Topological Co-Indices. Synergy: International Journal of Multidisciplinary Studies, 2(3), 1-9. https://doi.org/10.63960/SIJMDS-2025-2359

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