  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.

Mesoscale and Nanoscale Physics;Materials Science