Two-dimensional (2D) magnetic materials have arisen as viable contenders for next-generation nano-spintronics, quantum computing and high-density data storage technologies, owing to their distinctive magnetic and electrical characteristics at the atomic level. This study examines the molecular graph of a two-dimensional monolayer structure M3C12X12, where M represents a metal atom, C signifies carbon and X indicates a halogen atom. The molecule displays a Kagome lattice configuration, recognised for its unusual electrical properties. Employing graph-theoretic methodologies, we calculate several degree-based topological indices, such as the First Zagreb index, First hyper-Zagreb index, First and Second Gourava indices, Reciprocal Randic index, First and Second K-Banhatti indices and the Platt index. These indices function as molecular descriptors that measure structural characteristics pertinent to the compound’s physicochemical and magnetic properties. Our work illustrates the efficacy of topological indices in the structural characterisation of 2D materials and establishes a basis for further theoretical and computational investigations in materials science and nano-technology.