  Surface enhanced Raman scattering (SERS) exploits surface plasmons induced by
the incident field in metallic nanostructures to significantly increase the
Raman intensity. Graphene provides the ideal prototype two dimensional (2d)
test material to investigate SERS. Its Raman spectrum is well known, graphene
samples are entirely reproducible, height controllable down to the atomic
scale, and can be made virtually defect-free. We report SERS from graphene, by
depositing arrays of Au particles of well defined dimensions on
graphene/SiO$_2$(300nm)/Si. We detect significant enhancements at 633nm. To
elucidate the physics of SERS, we develop a quantitative analytical and
numerical theory. The 2d nature of graphene allows for a closed-form
description of the Raman enhancement. This scales with the nanoparticle cross
section, the fourth power of the Mie enhancement, and is inversely proportional
to the tenth power of the separation between graphene and the nanoparticle. One
consequence is that metallic nanodisks are an ideal embodiment for SERS in 2d.
