  We investigate the multiplicity of solutions for a generalized poly-Laplacian
system on weighted finite graphs and a generalized poly-Laplacian system with
Dirichlet boundary value on weighted locally finite graphs, respectively, via
the variational methods which are based on mountain pass theorem and
topological degree theory. We obtain that these two systems have a sequence of
minimax type solutions $\{(u_n,v_n)\}$ satisfying the energy functional
$\varphi(u_n,v_n)\to +\infty$ as $n\to +\infty$ and a sequence of local minimum
type solutions $\{(u_m^*,v_m^*)\}$ satisfying the energy functional
$\varphi(u_m^*,v_m^*)\to -\infty$ as $m\to +\infty$.
