  We study the emergence of synchronization in scale-free networks by
considering the Kuramoto model of coupled phase oscillators. The natural
frequencies of oscillators are assumed to be correlated with their degrees and
a time delay is included in the system. This assumption allows enhancing the
explosive transition to reach the synchronous state. We provide an analytical
treatment developed in a star graph which reproduces results obtained in
scale-free networks. Our findings have important implications in understanding
the synchronization of complex networks, since the time delay is present in
most systems due to the finite speed of the signal transmission over a
distance.
