[*999-3*]{} and [*555-11*]{} are respectively $17.49 eV$, $4.00 \mu_B$ and $11.91 eV$, $1.54 \mu_B$ (see, Table \[table2\]), which are much more higher than those given for tri-vacancy [*55-15*]{}.

  ------------------------------ ---------------------- -------------------------
           **Distance**           **Formation energy**    **Spin polarization**
   **(in interatomic dist. d)**         **(eV)**         **$(Q_{up}-Q_{down})$**
        \[0.5ex\] 1d (DV)                 5.76                     0.0
                2d                       13.027                   2.614
                3d                       13.197                   2.003
                4d                       13.547                   2.339
                5d                       13.435                   2.016
             \[1ex\]                                    
  ------------------------------ ---------------------- -------------------------

  : The formation energy and the total spin polarization for two vacancies in different positions shown in Figs. \[Vac2\].

\[table3\]

The tetra-vacancies of different configurations are depicted in Fig.\[Vac4\]. Among of all these configurations only one structure [*555-9*]{} containing three pentagon and one nonagon defects has the minimal formation energy $7.91~eV$ and zero magnetic moment (see, Table \[table2\]). The relaxed supercell and the band structure of [*555-9*]{} tetra-vacancy is depicted in Fig. \[Vac4\]a. The opposite spin-polarization bands of the [*555-9*]{} tetra-vacancy are highly degenerated. Furthermore, the Fermi energy in this case crosses the vacancy level yielding an extended state. Two other tetra-vacancy configurations, the relaxed supercells and the band structures of which are shown in Fig. \[Vac4\]b, and c, contain exactly the same defect structure [*5-12-5*]{} of two pentagons and one dodagon and have the same formation 