This year Nobel Prize award to the discovery of graphene has evidenced the relevance of this material, which has outstanding physical properties and promising technological applications.In the first µSR characterization of graphene we've observed a coherent muon spin precession,exceptionally persistent at high temperatures. We propose to extend this studyin order to definitely clarify the origin of the observed precession, consistent with bothlong range magnetic order and muon-hydrogen dipolar interactions, and to investigate its thermalevolution up to the highest possible tempratures. The effects of longitudinal applied fields will also be analysed.