  In this article, we prove a uniqueness result for a coefficient inverse
problems regarding a wave, a heat or a Schr\"odinger equation set on a
tree-shaped network, as well as the corresponding stability result of the
inverse problem for the wave equation. The objective is the determination of
the potential on each edge of the network from the additional measurement of
the solution at all but one external end-points. Our idea for proving the
uniqueness is to use a traditional approach in coefficient inverse problem by
Carleman estimate. Afterwards, using an observability estimate on the whole
network, we apply a compactness-uniqueness argument and prove the stability for
the wave inverse problem.
