We report a unique synthesis of single- and few-layer graphene films on carbon-doped Pt(83)Rh(17) surfaces by surface segregation and precipitation. The ultrathin graphene films were characterized by atomic force microscopy, Auger electron spectroscopy, and micro-Raman spectroscopy measurements, providing evidence of graphene film thickness and structural quality. The G and 2D band intensity images from micro-Raman spectroscopy measurements confirm that the graphene films with different coverage have very limited defects. Additionally, the 2D band peak can be well-fitted by a single Lozentian peak, indicating that graphene films are characteristic of single layer graphene. Graphene film thickness can be determined by analysis of Auger spectra, indicating that graphene films after 850 degrees C annealing mainly consist of monolayer graphene. By precise adjustment of annealing temperature, graphene film thickness and area size can be controlled and uniform large-area single-layer and double-layer graphene can be achieved.