  The Dirac equation is solved for triangular and hexagonal graphene quantum
dots for different boundary conditions in the presence of a perpendicular
magnetic field. We analyze the influence of the dot size and its geometry on
their energy spectrum. A comparison between the results obtained for graphene
dots with zigzag and armchair edges, as well as for infinite-mass boundary
condition, is presented and our results show that the type of graphene dot edge
and the choice of the appropriate boundary conditions have a very important
influence on the energy spectrum. The single particle energy levels are
calculated as function of an external perpendicular magnetic field which lifts
degeneracies. Comparing the energy spectra obtained from the tight-binding
approximation to those obtained from the continuum Dirac equation approach, we
verify that the behavior of the energies as function of the dot size or the
applied magnetic field are qualitatively similar, but in some cases
quantitative differences can exist.
