Understanding the connection of graphene with metal surfaces is a necessary step for developing atomically precise graphene-based technology. Combining high-resolution STM experiments and DFT calculations, we have unambiguously unveiled the atomic structure of the boundary between a graphene zigzag edge and a Pt(111) step. The graphene edges minimize their strain by inducing a 3-fold edge-reconstruction on the metal side. We show the existence of an unoccupied electronic state that is mostly localized on the C-edge atoms of one particular graphene sublattice, which could have implications in the design of graphene based devices.