  Motivated by recent experiments and a theoretical analysis of the gap
equation for the propagator of Dirac quasiparticles, we assume that the physics
underlying the recently observed removal of sublattice and spin degeneracies in
graphene in a strong magnetic field is connected with the generation of both
Dirac masses and spin gaps. The consequences of such a scenario for the
existence of the gapless edge states with zigzag and armchair boundary
conditions are discussed. In the case of graphene on a half-plane with a zigzag
edge, there are gapless edge states in the spectrum only when the spin gap
dominates over the mass gap. In the case of an armchair edge, however, the
existence of the gapless edge states depends on the specific type of mass gaps.

Mesoscale and Nanoscale Physics