  The quantum anomalous Hall effect can occur in single and few layer graphene
systems that have both exchange fields and spin-orbit coupling. In this paper,
we present a study of the quantum anomalous Hall effect in single-layer and
gated bilayer graphene systems with Rashba spin-orbit coupling. We compute
Berry curvatures at each valley point and find that for single-layer graphene
the Hall conductivity is quantized at $\sigma_{xy} = 2e^2/h$, with each valley
contributing a unit conductance and a corresponding chiral edge state. In
bilayer graphene, we find that the quantized anomalous Hall conductivity is
twice that of the single-layer case when the gate voltage $U$ is smaller than
the exchange field $M$, and zero otherwise. Although the Chern number vanishes
when $U > M$, the system still exhibits a quantized valley Hall effect, with
the edge states in opposite valleys propagating in opposite directions. The
possibility of tuning between different topological states with an external
gate voltage suggests possible graphene-based spintronics applications.
