▎ 摘　　要

In this paper, we compare the spectra of hulk and edge Hamiltonians on graphene from the point of view of the theory of quantum graphs. Since the bulk Hamiltonians with even potentials on the graphene has been studied by Kuchment and Post, our main targets here are the edge Hamiltonians on the graphene with boundaries. In this paper, we obtain their spectral properties under the Dirichlet boundary condition on the zigzag edges and draw pictures of the dispersion relation. Then, we obtain the existence of embedded eigenvalues for edge states in spectral bands.