Molecular topological indices are quantitative measurements that only take into account the topology of a compound’s molecular graph, disregarding any knowledge of the atom locations or chemical connections. An allotrope of carbon called graphene is composed of a single layer of atoms set up in a hexagonal lattice nanostructure. A single layer of carbon atoms organized in a honeycomb pattern make up the two-dimensional substance known as graphene. Graphene possesses significant inherent qualities like strong strength and great thermal and electrical conductivity. It is a sustainable substance with practically countless eco-friendly applications. In this study, we calculate the R molecular topological indices, S molecular topological indices, and Van molecular topological indices of graphene structure, taking into account all conceivable combinations of the number of rows and hexagons. There are high correlations between R, S Van index values and neighbourhood-based entropy values of graphene. This shows that these new indices can be used in QSPR/QSAR studies in chemistry and physics.