Let G=(V,E) be a finite weighted graph, and Ω⊆V be a domain such that Ω^∘≠∅. In this paper, we study the following initial boundary problem for the non-homogenous wave equation
∂^2_t u(t,x) − Δ_Ω u(t,x) = f(t,x), (t,x)∈[0,∞)×Ω^∘
u(0,x)=g(x), x∈Ω^∘,
∂_t u(0,x)=h(x), x∈Ω^∘,
u(t,x)=0, (t,x)∈[0,∞)×∂Ω,
where Δ_Ω denotes the Dirichlet Laplacian on Ω^∘. Using Rothe's method, we prove that the above wave equation has a unique solution.