OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 15 4 2025 08 31 Closed-Form Formulas for Classical and Reverse Degree-Based Topological Indices inTwo-Dimensional Grid Graphs 10.57647/ijm2c.2025.150425 EN Sara Shokrollahi Yancheshmeh https://orcid.org/0009-0007-9053-6982 Journal Article 2025 08 31 Topological indices are fundamental descriptors in mathematical chemistry, providing quantitative measures of molecular structure that correlate with physicochemical properties. This investigation presents a systematic computational approach to determineexa ct closed-form expressions for various degree-based topological indices appliedto two-dimensional grid networks Pm × Pn. We establish explicit formulas for classical Zagreb indices, Randić connectivity indices, atom-bond connectivity descriptors, geometric-arithmetic indices, harmonic indices, and the recently introduced reverse versions of these indices. Our methodology employs vertex degree distribution analysis combined with edge-based summation techniques to derive mathematically rigorous expressions. The obtained results demonstrate that grid networks exhibit predictable scaling behaviors for all examined indices, with computational complexity remaining polynomial in network dimensions. Moreover, for the first time, we provide a detailed graphical and comparative analysis of the specific degree-based topological indices addressed in this work and their reverse counterparts on grid networks, filling a gap in the literature by extending such comparisons beyond traditional molecular systems.