  The paper addresses boundary electronic properties of graphene with a complex
edge structure of the armchair/zigzag/armchair type. It is shown that the
finite zigzag region supports edge bound states with discrete equidistant
spectrum obtained from the Green's function of the continuum Dirac equation.
The energy levels exhibit the coupling between the valley degree of freedom and
the orbital quantum number, analogous to a spin-orbit interaction. The
characteristic feature of the spectrum is the presence of a zero mode, the
bound state of vanishing energy. It resides only in one of the graphene
valleys, breaking spontaneously Kramers' symmetry of the edge states. This
implies the spontaneous valley polarization characterized by the valley isospin
$\pm 1/2$. The polarization is manifested by a zero-magnetic field anomaly in
the local tunneling density of states, and is directly related to the local
electric Hall conductivity.
