  We present in this contribution a theoretical investigation of the
spontaneous emission and energy transfer rates between quantum systems placed
above a monolayer of conducting graphene. The conditions for strong and weak
coupling between a quantum system and the surface plasmon-polariton of graphene
are determined and, subsequently, we focus exclusively on the weak coupling
regime. We then calculate the dispersion relation of the surface plasmon mode
on graphene and, by varying the chemical potential, show a good control of its
resonance frequency. Using a Green's tensor formalism, we calculate the
spontaneous emission and energy transfer rates of quantum systems placed near
the graphene monolayer. The spontaneous emission rate of a single quantum
system is enhanced by several orders of magnitude close to the graphene
monolayer and we show that this enhancement is due almost exclusively to
excitation of the surface plasmon mode. When considering the energy transfer
rate between two quantum systems, we find a similar enhancement of several
orders of magnitude close to the graphene monolayer. The direct interaction
between the donor and acceptor dominates when they are close to each other, but
is modified from its free-space behavior due to the presence of the graphene
monolayer. As the donor-acceptor separation is increased, their direct
interaction is overshadowed by the interaction via the surface plasmon mode.
Due to the large propagation length of surface plasmon mode on graphene --
hundreds of nanometers -- this enhancement of the energy transfer rate holds
over large donor-acceptor separations along the graphene monolayer.
