  Standing waves near the zigzag and armchair edges, and their Berry's phases
are investigated. It is suggested that the Berry's phase for the standing wave
near the zigzag edge is trivial, while that near the armchair edge is
non-trivial. A non-trivial Berry's phase implies the presence of a singularity
in parameter space. We have confirmed that the Dirac singularity is absent
(present) in the parameter space for the standing wave near the zigzag
(armchair) edge. The absence of the Dirac singularity has a direct consequence
in the local density of states near the zigzag edge. The transport properties
of graphene nanoribbons observed by recent numerical simulations and
experiments are discussed from the point of view of the Berry's phases for the
standing waves.
