  We study the problem of the electron excitation spectrum in the presence of
point-like and regularized Coulomb impurities in gapped graphene. To this end,
we use the Dirac model and in the point-like case theory of self-adjoint
extensions of symmetric operators. In the point-like case, we construct a
family of self-adjoint Hamiltonians describing the excitations for any charge
of an impurity. Spectra and (generalized) eigenfunctions for all such
Hamiltonians are found. Then, we consider the spectral problem in the case of a
regularized Coulomb potential of impurities for a special regularization. We
study exact equations for charges of impurities that may generate bound states
with energy that coincides with the upper boundary of the negative branch of
the continuous spectrum (supercritical charges) and calculate these charges.
