A molecular graph, within the domain of chemistry, commonly represents the structure of a molecule graphically, with atoms as nodes and chemical bonds as edges connecting these nodes. Comprehending these structural representations is pivotal in pharmaceuticals for designing drugs, given that the arrangement of atoms and bonds significantly influences the molecule's properties . In this sense, a numerical value, irrespective of the particular node and edge labeling, which encapsulates specific characteristics of the molecular graph, is termed a graph invariant or topological index. Hence, various topological indices and their mathematical properties have been explored . In particular, the Randić index emerges as the foremost extensively studied, commonly employed, and broadly acknowledged topological index ; this is due to its close correlation with numerous chemical properties, including boiling points, surface area, solubility in water of alkanes . It was initially termed as the "branching index" when introduced by chemist Milan Randić in 1975 as