  We analyze the bound-state spectra of mass-profile quantum dots in graphene,
a system at current experimental reach. Homogeneous perpendicular magnetic
fields are also considered which result in breaking the valley degeneracy. The
spectra show rich features, arising from the chiral band structure of graphene
and its Landau levels and we identify three different regimes depending on the
ratio between the radius of the dot and the magnetic length. We further carry
out a comparison with potential-well quantum dots discussed in [Recher et al,
Phys. Rev. B 79, 085407 (2009)] and conclude that mass confinement may offer
significant advantages for optical applications in the THz and infrared regime.
Also due to experimental advances, we additionally analyze the band structure
of a linear chain of mass-profile quantum dots, where overlap-assisted hopping
processes play a main role for closely packed arrays. Here, the inclusion of
Coulomb interactions shows that Frenkel excitons can be hosted by the system
for certain values of the lattice constant. A Bose-Hubbard model can be
mimicked under such a choice of the distance between the dots.
