The wave vector is a vector which points in the direction of propagation of the wave. In contrast to the electromagnetic waves the wave vector, k, of lattice vibrations has discrete spectrum within defined limits. The possible values of k depend on the boundary conditions. Now we can see that dispersion relation is not strictly speaking a continuous curve but rather a series of closely spaced points representing the possible modes of vibrations.
Figure below is the dispersion relation for diatomic linear lattice.
The spacing between the dots is equal to where N is the number of atoms in the lattice.