We consider functions on a graph $G$ whose evolution in time $-\infty<t<\infty$ is governed by a Schr\"{ o}dinger type equation with a combinatorial Laplace operator on the right side. For a given subset $S$ of vertices of $G$ we compute a cut-off frequency $\omega>0$ such that solutions to a Cauchy problem with initial data in $PW_{ \omega}(G)$ are completely determined by their samples on $S\times \{ k\pi/\omega\},$ where $k\in \mathbf{ N}$. It is shown that in the case of a bipartite graph our results are sharp.
Categories: math.SP