  In this paper, we consider the Schr\"odinger type equation $-\Delta
u+V(x)u=f(x,u)$ on the lattice graph $\mathbb{Z}^{N}$ with indefinite
variational functional, where $-\Delta$ is the discrete Laplacian.
Specifically, we assume that $V(x)$ and $f(x,u)$ are periodic in $x$, $f$
satisfies some growth condition and 0 lies in a spectral gap of $(-\Delta +
V)$. We obtain ground state solutions by using the method of generalized Nehari
manifold which has been introduced in arXiv:1801.06872.
