  We study edges states of graphene ribbons in the quantized Hall regime, and
show that they can be described within a continuum model (the Dirac equation)
when appropriate boundary conditions are adopted. The two simplest
terminations, zigzag and armchair edges, are studied in detail. For zigzag
edges, we find that the lowest Landau level states terminate in two types of
edge states, dispersionless and current-carrying surface states. The latter
involve components on different sublattices that may be separated by distances
far greater than the magnetic length. For armchair edges, the boundary
conditions are met by admixing states from different valleys, and we show that
this leads to a single set of edges states for the lowest Landau level and two
sets for all higher Landau levels. In both cases, the resulting Hall
conductance step for the lowest Landau level is half that between higher Landau
levels, as observed in experiment.
