  The periodic Schrodinger operator $ H $ on a discrete periodic graph is
considered. We estimate the discrete spectrum of the perturbed operator $ H _
{-} (t) = H-tV $, $ t> 0 $, where the potential $ V \ ge 0 $ is decreasing and
$t>0$ is the coupling constant. If the potential has a power asymptotics at
infinity, then we obtain asymptotics of the discrete spectrum of operator $ H_
{-} (t) $ with a large coupling constant.
