Determining Topological Indices of Sheet Oxide Network Using Bi-Distance Technique

Abstract

Topological indices are numerical invariants that capture the structural properties of graphs, playing a crucial role in quantitative structure-activity relationships (QSARs) by linking molecular structures to their biological activities. This research investigates Bi-distance degree-based topological descriptors, such as the Bi-distance atom bond connectivity index, Randić index, geometric arithmetic index, hyper Zagreb index, forgotten index, first and second Zagreb indices, Zagreb augmented index, and redefined Zagreb indices, applied to sheet oxide network. By partitioning edge sets based on degree and cardinality, these indices are computed using combinatorial methods. The findings reveal that the Zagreb indices, atom bond connectivity index, and forgotten index can be effectively determined using the Bi-distance approach, offering a novel perspective for analyzing molecular structures. This research aims to provide insights into the biological activities and physical properties of oxide molecule, with potential applications in pharmaceutical and biological networks. The study highlights the significance of topological indices in graph theory for examining the structural characteristics of chemical compounds, contributing to a deeper understanding of their properties and behaviors.