  The Sturm-Liouville operator on a star-shaped graph is considered. We assume
that the potential is known a priori on all the edges except one, and study the
partial inverse problem, which consists in recovering the potential on the
remaining edge from the part of the spectrum. A constructive method is
developed for the solution of this problem, based on the Riesz-basicity of some
sequence of vector functions. The local solvability of the inverse problem and
the stability of its solution are proved.
