  We consider discrete Schr\"odinger operators with periodic potentials on
periodic graphs perturbed by guided non-positive potentials, which are periodic
in some directions and finitely supported in other ones. The spectrum of the
unperturbed operator is a union of a finite number of non-degenerate bands and
eigenvalues of infinite multiplicity. We show that the spectrum of the
perturbed operator consists of the unperturbed one plus the additional guided
spectrum, which is a union of a finite number of bands. We estimate the
position of the guided bands and their length in terms of graph geometric
parameters. We also determine the asymptotics of the guided bands for large
guided potentials. Moreover, we show that the possible number of the guided
bands, their length and position can be rather arbitrary for some specific
potentials.
