of the ’odd distance’ vacancy and the reference vacancy belong to the different sublattices (see, Figs. \[Vac2\]c and $e$). According to the Lieb’s rule, the magnetization in the first case should be finite, whereas in the second case it should be zero. The formation energies and the magnetizations of different two-vacancy topologies are presented in Table \[table3\]. As it is seen from Fig. \[Vac2\], all relaxed supercell structures contain two pentagon-nonagon [*5-9*]{} defects, each of which is typical of a mono-vacancy in Fig. \[Vac1\]a, even when two vacancies are located in $1d$ distance. Two vacancies in larger distance do not interact practically each other, and the formation energies as well as the magnetizations become approximately two times higher than that of a mono-vacancy.

[cc]{}\

All the two-vacancy structures (in Fig. \[Vac2\]) except a di-vacancy in Fig. \[Vac1\]b have dangling bonds. Consequently, the local DOS of DV for spin-up and spin-down states, shown in Fig. \[Vac1\]b correspondingly by red (above zero) and blue (below zero) curves, coincides completely at each points. The local DOS corresponding to two opposite spin polarizations for all other vacancy configurations, presented in Figs. \[Vac2\], differ each other due to existence of the dangling bonds. The magnetization 