Application of the Nirmala Index in Nanotechnology: Optimizing Molecular Structures for Advanced Nanomaterials

Abstract Chemical graph theory has played a key role in advancing our understanding of molecular structure by producing degree-based topological indices that forecast crucial physical and chemical properties. In this paper we attempt to investigate this recently defined Nirmala index as an invariant from different topological angles and applications on multiple molecular graph structures such as triangular, double, and alternate quadrilateral snake structures. This index offers a more profound comprehension of the connections between molecular structures and attributes. The next generation of ground breaking developments in nanotechnology, where the creation of devices and functional nanomaterials hinges on molecular interaction at the nanoscale, may also be greatly influenced by this index. These indices have potential applications in drug delivery systems and in molecular structure optimization related to nanotechnological fields like nanophotonics and nanoelectronics. Consequently, the Nirmala index will pave the way for the development of more sophisticated tools for the production of high-performing nanoscale materials.