  We study theoretically the Kondo effect for a magnetic adatom on graphene
using the Anderson model.Upon obtaining the Green's function of the impurity to
higher order contributions in the hybridization, we calculated analytically the
selfenergy in the presence of strong correlations.It is found that the Kondo
resonance takes place in a narrow energy range of the impurity level around the
Fermi energy which can be tuned by a gate voltage.We show that this range is
linear in the Fermi energy $|\mu|$ and is significantly narrower than in the
case for a normal metal.The origin of this behavior is traced back to the
inherent properties of graphene, especially its linear dispersion.The
singularity in the full Green's function is also analyzed with the help of a
transparent geometrical method.The relations between the various selfenergies
and the implications for the experimental observations are discussed .
