  We study the synchronization of R{\"o}ssler oscillators as prototype of
chaotic systems, when they are coupled on scale-free complex networks. We find
that the underlying topology crucially affects the global synchronization
properties. Especially, we show that the existence of loops facilitates the
synchronizability of the system, whereas R\"ossler oscillators do not
synchronize on tree-like topologies beyond a certain size. By considering
Cayley trees, modified by various shortcuts, we find that also the distribution
of shortest path lengths between two oscillators plays an important role for
the global synchronization.
