  The phonon density of states (DOS) of graphene with different types of point
defects (carbon isotopes, substitution atoms, vacancies) is considered. Using a
solvable model which is based on the harmonic approximation and the assumption
that the elastic forces act only between nearest neighboring ions we calculate
corrections to graphene DOS dependent on type and concentration of defects. In
particular the correction due to isotopic dimers is determined. It is shown
that a relatively small concentration of defects may lead to significant and
specific changes in the DOS, especially at low frequencies, near the Van Hove
points and in the vicinity of the K-points of the Brillouin zone. In some cases
defects generate one or several narrow gaps near the critical points of the
phonon DOS as well as resonance states in the Brillouin zone regular points.
All types of defects are characterized by the appearance of one or more
additional Van Hove peaks near the (Dirac) K points and their singular
contribution may be comparable with the effect of electron-phonon interaction.
Besides, for low frequencies and near the critical points the relative change
in density of states may be many times higher than the concentration of
defects.
