  Taking into account the possibility of a p-wave hybridization function
$V(\vec k)$ of ad-atom with Dirac electrons in graphene -- which arises for
vacancies and hollow-site impurities -- we study the nature of magnetic moment
formation within the single impurity Anderson model (SIAM). Compared to the
s-wave hybridization function, we find that the local moments formed within the
Hartree mean field are robust against the change in the parameters of the
model. Further we investigate the stability of the local moments with respect
to quantum fluctuations by going beyond the Hartree approximation. We find that
for parameter regimes where local moments formed by top-site ad-atoms are
completely washed out by quantum fluctuations, those formed by vacancies (or
hollow-site impurities) survive the quantum fluctuations captured by
post-Hartree approximation. Hence vacancies and hollow-site ad-atoms are
suitable candidates to produce stable local moments.
