  As a particular application of the earlier proposed model of graphene as a
macromolecule, we found the exact analytical expression of dispersion relation
for the band of edge states in graphene zigzag ribbons. This band is often
referred to as "dispersionless band" or "zero mode". The obtained result
contrasts description of edge states given in the referenced paper, showing
that the earlier given explanation is valid only for a very narrow region of
values of the electron/hole wave vector, but for the rest, it is not correct.
