  We obtain the solution of the Dirac equation in (2+1) dimensions in the
presence of a constant magnetic field normal to the plane together with a
two-dimensional Dirac-oscillator potential coupling. We study the energy
spectrum of graphene quantum dot (QD) defined by electrostatic gates. We give
discussions of our results based on different physical settings, whether the
cyclotron frequency is similar or larger/smaller compared to the oscillator
frequency. This defines an effective magnetic field that produces the effective
quantized Landau levels. We study analytically such field in gate-tunable
graphene QD and show that our structure allow us to control the valley
degeneracy. Finally, we compare our results with already published work and
also discuss the possible applications of such QD.
