  We numerically investigate the effect of Klein tunneling on the Aharonov-Bohm
oscillations in graphene rings using a tight-binding model with
nearest-neighbor couplings. In order to introduce Klein tunneling into the
system, we apply an electrostatic potential to one of the arms of the ring,
such that this arm together with the two adjacent leads form either a $nn'n$-
or $npn$-junction ($n,n'$: conduction band transport, $p$: valence band
transport). The former case corresponds to normal tunneling and the latter case
to Klein tunneling. We find that the transmission properties strongly depend on
the smoothness of the $pn$-interfaces. In particular, for sharp junctions the
amplitude profile is symmetric around the charge neutrality point in the gated
arm, whereas for smooth junctions the Aharonov-Bohm oscillations are strongly
suppressed in the Klein tunneling as compared to the normal tunneling regime.
