  We study theoretically the effects of short-range electron-electron
interactions on the electronic structure of graphene, in the presence of single
substitutional impurities. Our computational approach is based on the $\pi$
orbital tight-binding approximation for graphene, with the electron-electron
interactions treated self-consistently at the level of the mean-field Hubbard
model. We compare explicitly non-interacting and interacting cases with varying
interaction strength and impurity potential strength. We focus in particular on
the interaction-induced modifications in the local density of states around the
impurity, which is a quantity that can be directly probed by scanning tunneling
spectroscopy of doped graphene. We find that the resonant character of the
impurity states near the Fermi level is enhanced by the interactions.
Furthermore, the size of the energy gap, which opens at high-symmetry points of
the Brillouin zone of the supercell upon doping, is significantly affected by
the interactions. The details of this effect depend subtly on the supercell
geometry. We use a perturbative model to explain these features and find
quantitative agreement with numerical results.
