  There are two types of edge states in graphene with/without magnetic field.
One is a quantum Hall edge state, which is topologically protected against
small perturbation. The other is a chiral zero mode that is localized near the
boundary with/without magnetic field. The latter is also topological but is
guaranteed to be zero energy by the chiral symmetry, which is also responsible
for massless Dirac like dispersion. Conceptual roles of the edge states are
stressed and reviewed from a view point of the bulk-edge correspondence and the
topological order.
