  We study Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional
regular topologies with nearest neighbor interactions.
  We derive the analytical expressions for the common frequency in the case of
phase-locked motion and for the critical frequency of the pacemaker, placed at
an arbitrary position in the lattice, so that above the critical frequency no
phase-locked motion is possible. We show that the mere change in topology from
an open chain to a ring induces synchronization for a certain range of
pacemaker frequencies and couplings, while keeping the other parameters fixed.
Moreover we demonstrate numerically that the critical frequency of the
pacemaker decreases as a power of the linear size of the lattice with an
exponent equal to the dimension of the system. This leads in particular to the
conclusion that for infinite-dimensional topologies the critical frequency for
having entrainment decreases exponentially with the size of the system, or,
more generally, with the depth of the network, that is the average distance of
the oscillators from the pacemaker.
