Abstract
Graphene grown on substrates ordinarily have defects in its structure. Such defects affect the electronic properties of graphene. In this report, the atomic structures of graphene having a monovacancy or a multivacancy are equilibrated using first-principles calculations. The formation energies and bandgaps of the equilibrated structures are compared with each other. It is shown that the formation energy ofa 555-777 divacancy is the lowest, and that graphene with some kinds of defects can have nonzero bandgaps.