IRREGULARITY TOPOLOGICAL INDEX OF A NANOROD GRAPH

Abstract

Nanostructures have revolutionized modern science and technology, offering novel properties and applications in electronics, medicine, energy storage and catalysis. One way to model and analyze the structural properties of nanomaterials is through graph theory. In particular, topological indices derived from graph representations of nanostructures provide valuable insights into their chemical reactivity, stability and other physicochemical properties. In recent years, irregularity indices have gained prominences an important class of topological indices. These indices quantify the deviation from regularity in a graph, which can be linked to molecular instability or asymmetry in nanostructures. The discovery of fullerenes and carbon nanotubes (CNTs) led to the irregular molecular graphs [5]. Various irregularity indices such as Albertson’s irregularity index, variance of degrees, total irregularity, IRL and IRM indices have been proposed and studied extensively in graph theory and mathematical chemistry.Quantifying the irregularity of graphs is a fundamental concept in numerous scientific disciplines, including chemistry and network theory.