(color online) (a) PDOS of the pristine graphene and the graphene with different vacancy defects SV, DV, TV, and QV. For clarity, the curves from up to down are shifted up by 0.045, 0.030, 0.015, and 0, respetively. The filled and open circles stand for the atom vibration amplitudes of the pristine and QV graphenes with respect to the distance from the vacancies for (b) the low acoustic mode (ω = 0) and (c) the highest optical mode (ω = 1599.9 cm⁻¹, 1599.5 cm⁻¹) at Γ point.