  We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on
simplest graphs. Formulation of the problem and exact analytical solutions of
NLSE are presented for star graphs consisting of three bonds. It is shown that
the method can be extended for the case of arbitrary number of bonds of star
graphs and for other simplest topologies such as tree and loop graphs. The case
of repulsive and attractive nonlinearities are treated separately.
