  We examine the exchange Hamiltonian for magnetic adatoms in graphene with
localized inner shell states. On symmetry grounds, we predict the existence of
a class of orbitals that lead to a distinct class of quantum critical points in
graphene, where the Kondo temperature scales as $T_{K}\propto|J-J_{c}|^{1/3}$
near the critical coupling $J_{c}$, and the local spin is effectively screened
by a \emph{super-ohmic} bath. For this class, the RKKY interaction decays
spatially with a fast power law $\sim1/R^{7}$. Away from half filling, we show
that the exchange coupling in graphene can be controlled across the quantum
critical region by gating. We propose that the vicinity of the Kondo quantum
critical point can be directly accessed with scanning tunneling probes and
gating.
