  We investigate the energy spectrum, wave functions, and local density of
states of an electrical dipole placed on a sheet of gapped graphene as function
of the charge strength Z{\alpha} for different sizes of the dipole and for
different regularization parameters. The dipole is modeled as consisting of a
positive and negative charge. Bound states are found within the gap region with
some energy levels that anticross and others that cross as function of the
impurity strength Z{\alpha}. The anticrossings are more pronounced and move to
higher charges Z{\alpha} when the length of the dipole decreases. These energy
levels turn into atomic collapse states when they enter the positive (or
negative) energy continuum. A smooth transition from the single-impurity
behavior to the dipole one is observed: The states diving towards the continuum
in the single-impurity case are gradually replaced by a series of anticrossings
that represent a continuation of the diving states in the single-impurity case.
By studying the local density of states at the edge of the dipole we show how
the series of anticrossings persist in the positive and negative continuum.
