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

The periodic Schrödinger operator $ H$ on a discrete periodic graph is treated. The discrete spectrum is estimated for the perturbed operator $ H_{\pm }(t)=H\pm tV$, $ t>0$, where $ V\ge 0$ is a decaying potential. In the case when the potential has a power asymptotics at infinity, an asymptotics is obtained for the discrete spectrum of the operator $ H_{\pm }(t)$ for a large coupling constant.