  A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is
shown that functions from some of these spaces are uniquely determined by their
values on some sets of vertices which are called the uniqueness sets. Such
uniqueness sets are described in terms of Poincare-Wirtingertype inequalities.
A reconstruction algorithm of Paley-Wiener functions from uniqueness sets which
uses the idea of frames in Hilbert spaces is developed. Special consideration
is given to n-dimensional lattice, homogeneous trees, and eigenvalue and
eigenfunction problems on finite graphs.
