Sampling solutions of Schrödinger equations on combinatorial graphs

We consider functions on a graph $G$ whose evolution in time $-\infty<t<\infty$ is governed by a Schrödinger 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 $ω>0$ such that solutions to a Cauchy problem with initial data in $PW_ω(G)$ are completely determined by their samples on $S\times \{kπ/ω\},$ where $k\in \mathbf{N}$. It is shown that in the case of a bipartite graph our results are sharp.

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