M-Polynomials and degree-based topological indices of the two dimensional Coronene fractal structures

Topological indices are numerical descriptors widely used to investigate the structural, physical, and chemical properties of molecular compounds. Among them, degree-based topological indices have demonstrated strong correlations with a variety of molecular characteristics, making them a central topic in chemical graph theory. The M-polynomial serves as a powerful generating function for deriving such indices. In this study, we present closed-form expressions for several important degree-based topological indices associated with the zigzag molecular graph of two-dimensional coronene fractal structures. The indices examined include the first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randic index, the inverse Randic index, and the augmented Zagreb index. The derivations are carried out using a calculus-based approach, offering deeper insights into the topological and structural features of these nanostructures.