  We theoretically investigate the spectrum of a single electron double quantum
dot, defined by top gates in a graphene with a substrate induced gap. We
examine the effects of electric and magnetic fields on the spectrum of
localized states, focusing on the tunability of the inter-dot coupling. We find
that the substrate induced gap allows for electrostatic control, with some
limitations that for a fixed inter-dot distance, the inter-dot coupling can not
be made arbitrarily small due to the Klein tunneling. On the other hand, the
proximity of the valence band in graphene allows for new regimes, such as an
$npn$ double dot, which have no counterparts in GaAs.
