Sampling solutions of Schro¨dinger equations on combinatorial graphs

We consider functions on a graph G whose evolution in time - ∞ <; t <; ∞ 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 x {kπ /ω}, where k ε N. It is shown that in the case of a bipartite graph our results are sharp.