In this paper, we study the following p-Laplacian equation \(\begin{aligned} -\Delta _{p} u+h(x)|u|^{p-2} u=\left( R_{\alpha } *F(u)\right) f(u) \end{aligned}\) on lattice graphs \(\mathbb {Z}^N\) , where \(p\ge 2\) , \(\alpha \in (0,N)\) are constants and \(R_{\alpha }\) is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under different assumptions on potential function h, we prove the existence of ground state solutions respectively by the methods of Nehari manifold.
