  We present a framework to solve the open problem of formulating the inverse
scattering method (ISM) for an integrable PDE on a star-graph. The idea is to
map the problem on the graph to a matrix initial-boundary value (IBV) problem
and then to extend the unified method of Fokas to such a matrix IBV problem.
The nonlinear Schr\"odinger equation is chosen to illustrate the method. The
framework unifies all previously known examples which are recovered as
particular cases. The case of general Robin conditions at the vertex is
discussed: the notion of linearizable initial-boundary conditions is
introduced. For such conditions, the method is shown to be as efficient as the
ISM on the full-line.
