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Journal of Polymer & Composites Original Research Special issue

Computational Study of Sombor Index on Generalized Abid–Waheed Graphs for Polymer Modeling

  1. Ramani M. S Department of Mathematics, M.O.P. Vaishnav College for Women, Chennai
  2. Senbagamalar. J Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai
  3. N. Kumaran Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai

Abstract

This study investigates the topological properties of generalized Abid Waheed graphs. Development of theoretical models in chemistry, reducing computational complexity while analysing large molecules or networks Abid Waheed graphs play a significant role. Motivated by these findings, the research was extended to encompass generalized Abid Waheed graphs, characterized by r cycles of order s. A notable similarity between Abid Waheed graphs and Jahangir graphs was observed. The potential applications of these findings in network topology and optimization are explored, leveraging the degree-based indices on Abid Waheed graphs as a model for networking systems. In this study, we further examined the topological characteristics of nano star dendrimers through the framework of chemical graph theory by employing Abid Waheed graph models. Nano star dendrimers, a class of star-shaped polymers, possess highly branched and symmetrical structures, making them particularly well-suited for mathematical representation via recursive and hierarchical graphs. Abid Waheed graphs, recognized for effectively capturing the complexity of molecular architectures, were adapted to model various generations of such dendritic polymers. Our analysis focused on two significant graph-theoretic descriptors: the Sombor index, introduced by Gutman et al. in 2021, and the M-polynomial. The Sombor index, defined as: Our findings reveal that both the Sombor index and the M-polynomial are responsive to structural variations in dendrimer generations, displaying consistent and interpretable growth patterns as the dendritic network expands. This work establishes a novel and meaningful connection between topological indices and polymer nanostructures, contributing to the development of computational tools for predicting physicochemical properties and supporting applications in nanomaterial design, drug delivery, and materials science. Furthermore, the Sombor index, through the encoding of degree-based structural properties, is a sensitive indicator of molecular complexity and branching that are directly linked to the physicochemical behaviour of dendritic polymers including nano star dendrimers.

Keywords

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