  We propose a generalized Dirac fermion description for the electronic state
of graphene terminated by a zigzag edge. This description admits a spin-orbit
coupling needed to preserve time-reversal invariance of the zigzag confinement,
otherwise, for spinless particles, showing the parity anomaly typical of
quantum electrodynamics in (2+1) dimensions. At a certain critical strength the
spin-orbit coupling induces a phase transition of the quantum-spin-Hall type.
It is manifested by a novel type of the edge states consisting of a Kramers'
pair of counter-propagating modes with opposite spin orientations. Such edge
states are capable of accumulating an integer spin in response to a transverse
electric field in the absence of a magnetic one. They exist without any
excitation gap in the bulk, due to which our system stands out among other
quantum spin Hall systems studied earlier. We show that at the transition the
local density of states is discontinuous and its energy dependence reflects the
phase diagram of the system.
