  The valley-Chern and spin-valley-Chern numbers are the key concepts in
valleytronics. They are topological numbers in the Dirac theory but not in the
tight-binding model. We analyze the bulk-edge correspondence between the two
phases which have the same Chern and spin-Chern numbers but different
valley-Chern and spin-valley-Chern numbers. The edge state between them is
topologically trivial in the tight-binding model but is shown to be as robust
as the topological edge. We construct Y-junctions made of topological edges.
They satisfy the topological Kirchhoff law, where the topological charges are
conserved at the junction. We may interpret a Y-junction as a scattering
process of particles which have four topological numbers. It would be a
milestone of future topological electronics.
