The structure of a single-layer graphene on Ru(0001) is compared with that of a single-layer hexagonal boron nitride nanomesh on Ru(0001). Both are corrugated sp2 hybridized networks and display a π band gap at the K̅ point of their 1×1 Brillouin zone. In contrast to h-BN/Ru(0001), g/Ru(0001) has a distinct Fermi surface. Together with the band structure measurements this indicates that 0.1e per 1×1 unit cell are transferred from the Ru substrate to the graphene. Photoemission from adsorbed xenon on g/Ru(0001) identifies two Xe 5p1/2 lines, separated by 240 meV, which reveals a corrugated electrostatic potential energy surface like on h-BN/Rh(111). These two Xe species are related to the topography of the template and have different desorption energies.