  Quantum dots induced by a strong magnetic field applied to a single layer of
graphene in the perpendicular direction are investigated. The dot is defined by
a model potential which consists of a well of depth $\Delta V$ relative to a
flat asymptotic part and quantum states formed from the zeroth Landau level are
considered. The energy of the dot states cannot be lower than $-\Delta V$
relative to the asymptotic potential. Consequently, when $\Delta V$ is chosen
to be about half of the gap between the zeroth and first Landau levels, the dot
states are isolated energetically in the gap between Landau level 0 and Landau
level -1. This is confirmed with numerical calculations of the magnetic field
dependent energy spectrum and the quantum states. Remarkably, an antidot formed
by reversing the sign of $\Delta V$ also confines electrons but in the energy
region between Landau level 0 and Landau level +1. This unusual behaviour gives
an unambiguous signal of the novel physics of graphene quantum dots.
