  We investigate theoretically the magnetic levels and optical properties of
zigzag- and armchair-edged hexagonal graphene quantum dots (GQDs) utilizing the
tight-binding method. A new bound edge state at zero energy appears for the
zigzag GQDs in the absence of a magnetic field. The magnetic levels of GQDs
exhibit a Hofstadter-butterfly spectrum and approach the Landau levels of
two-dimensional graphene as the magnetic field increases. The optical
properties are tuned by the size, the type of the edge, and the external
magnetic field.
