Topological Indices on Subdivided Graphs of Different Chemical Networks

Abstract

This thesis offers a thorough analysis of topological indices derived from graph theory, with a specific focus on the Subdivided Chain Silicates and Honeycomb Networks. We explore a broad range of vertex degree and vertex neighborhood degree sum topological indices. The work explores indexes such as the Randic, General Randic, General Inverse Randic, Sombor, General Sombor, Harmonic, Geometric-Arithmetic, Hyper-Zagreb, Re-defined Zagreb, Augmented Zagreb, Atomic-bond Connectivity, Gourava and Hyper-Gourava, Symmetric Division Degree and numerous Kulli-Basava variants. These indices are computed analytically for subdivided chain silicates and honeycomb networks configurations with n-dimensions. These results demonstrate the structural distinctiveness and possible chemical characteristics of these networks, providing important information for use in medication development, chemical compound analysis, and nanotechnology. By developing new mathematical formulations and increasing the prediction capacity of topological indicators in nano-material science, this study advances chemical graph theory.