  This paper studies the synchronization of a finite number of Kuramoto
oscillators in a frequency-dependent bidirectional tree network. We assume that
the coupling strength of each link in each direction is equal to the product of
a common coefficient and the exogenous frequency of its corresponding head
oscillator. We derive a sufficient condition for the common coupling strength
in order to guarantee frequency synchronization in tree networks. Moreover, we
discuss the dependency of the obtained bound on both the graph structure and
the way that exogenous frequencies are distributed. Further, we present an
application of the obtained result by means of an event-triggered algorithm for
achieving frequency synchronization in a star network assuming that the common
coupling coefficient is given.
