  Taking into account the constraints imposed by the lattice symmetry, the
phonon dispersion is calculated for graphene with interactions between the
first and second nearest neighbors in the framework of the Born-von Karman
model. Analytical expressions are obtained for the out-of-plane (bending) modes
determined only by two force constants as well as for the in-plane modes with
four force constants. Values of the force constants are found in fitting to
elastic constants and Raman frequencies observed in graphite.
