carbon structure.

Although many effects observed in graphene are attributed to the presence of vacancies and defects, we will focus here particularly on a magnetic response and self-repairing of graphene in the presence of vacancies.

Magnetic response associated with vacancies produced by the irradiation of graphene with high-energy protons and carbon ($C^{4+}$) ions has been studied recently as experimentally [@ubgg10; @whsz09; @ckf09] as well as theoretically [@yh07; @yazyev10; @mlfn04; @ztkv07; @bkk11; @py12; @cwtd15] by means of he molecular dynamics simulations and DFT based [*ab-initio*]{} methods. Many experimental observations reported in the literature provide inconsistent even contradictory results. Experimental evidence of ferromagnetic order has been observed [@whsz09] in irradiated graphene, the origin of which was suggested by the authors to be the defects located in the structure. Magnetic ordering was mainly observed in graphitic materials [@ckf09], which was explained by the existence of the localized electronic states at grain boundaries of highly oriented defective pyrolytic graphite. Some observation of ferromagnetism even anti-ferromagnetism seems to be artifacts.

[*Ab-initio*]{} density-functional theory (DFT) investigations of magnetization produced by vacancies in a graphene are mainly performed [@yazyev10; @mlfn04; @cs06; @ztkv07; @bkk11; @py12; @cwtd15; @czll11] by a superlattice method, where a vacancy is created in a 