(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Iterative graph have several applications in social network analysis, optimization problems, machine learning, and game theory. Such graphs are also commonly used in chemistry, physics, and mathematics. In this article, we derive the M-polynomial for the fractal growth patterns of benzene (F GBn, n ≥ 1), the Pythagoras tree (P Tn, n ≥ 1), and the benzene dendrimer (DBn, n ≥ 2). Moreover, we compute some degree-based topological indices based on the M-polynomials, such as the first Zagreb index, the second Zagreb index, the modified second Zagreb index, the general Randi ́c index, the harmonic index, the inverse sum index, and the symmetric division degree index. Finally, we presented our work graphically and compared the sketches of M-polynomials and degree-based topological indices.