Comparative study of the nature of chemical bonding of corrugated graphene on Ru(0001) and Rh(111) by electronic structure calculations

► Morphology of graphene on transition metal by DFT. ► Hybridization of graphene \pi orbitals with metallic d band. ► Pore and wire structure of g/Rh(111) nanomesh. ► Perspective of g/Rh as template for trapping molecules.