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As a particular application of the earlier proposed model of graphene as amacromolecule, we found the exact analytical expression of dispersion relationfor the band of edge states in graphene zigzag ribbons. This band is oftenreferred to as "dispersionless band" or "zero mode". The obtained resultcontrasts description of edge states given in the referenced paper, showingthat the earlier given explanation is valid only for a very narrow region ofvalues of the electron/hole wave vector, but for the rest, it is not correct.

Dispersion of "Dispersionless Zero Mode": Comments on L. Brey and H.A.  Fertig paper Electronic States of Graphene Nanoribbons Studied With The Dirac  Equation