  We study theoretically the physical properties of a magnetic impurity in
graphene. Within the Anderson model for a very strong Coulomb interaction on
the impurity, we start from the Slave-Boson method and introduce a topological
picture consisting of a degree of a map and a winding number (WN) to analyze
the phase shift and the occupation on the impurity. The occupation is linked to
WN. For a generic normal metal we find a fractional WN. In contrast, the
winding is accelerated by the relativistic dispersion of graphene at
half-filling leading to an integer occupation. We show that the renormalization
parameter that shifts the impurity level is insufficient to invert the sign of
the energy level. Consequently, the state at half-filling is stable unless a
gate voltage is tuned such that the Fermi level touches the edge of the
broadened impurity level. Only in this case the zero field susceptibility is
finite and shows a pronounced peak structure with the gate voltage.
