  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.
