  We employ the Green's function technique to investigate the vacancy-induced
quasi-localized magnetic moment formation in mono-layer graphene starting with
the Dirac Hamiltonian, which focuses on the {\pi}- orbitals only, involving the
nearest neighbor(NN)(t) and moderate second neighbor(SN)(t' < t/3) hopping
integrals. The vacancy defect is modeled by the addition of the on-site
perturbation potential to the Hamiltonian. We find that, when (t'/t) << 1, the
vacancy induced {\pi}-state at the zero of energy(zero-mode state(ZMS)) does
not inhabit the minority sub-lattice due to the strong scalar potential induced
by the vacancy(the ZMSs get lodged in the majority sub-lattice) whereas, when
(t'/t) is increased, the ZMS is somewhat suppressed. This shows that, not only
the shift of the Fermi energy away from the linearly-dispersive Dirac points,
the issue of this topological localization is also hinged on the ratio (t'/t).
Furthermore, when a vacancy is present, the three sp2- hybridized {\sigma}
states of each of the three nearest-neighbor carbon atoms, forming a carbon
triangle surrounding the vacancy, are close to the Fermi energy (EF). The
Hund's coupling between these {\sigma} electrons and the remaining electron
which occupies the {\pi} state spin polarizes the {\pi} state leading to local
moment formation close to EF. Since the system at the Fermi level has low
electronic density, there is poor screening of such magnetic moments. This may
lead to a high Curie temperature for such vacancy-induced moments.
