Graphene is one of the most promising nanomaterial because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and bio devices. Inspired by recent work on Graphene of computing topological indices, here we compute new topological indices viz. Arithmetic-Geometric index ( AG 2 index), SK 3 index and Sanskruti index of a molecular graph G and obtain the explicit formulae of these indices for Graphene.