Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graph

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 $,wherethepotential$ V \ ge 0 $isdecreasingand$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.