The wave equation on a finite weighted graph does have a unique solution, but the paper's explicit solution formula is wrong and its infinite propagation speed theorem rests on an impossible eigenfunction assumption.
F.-C., Ngai, S.-M., Teplyaev, A.: One-dimensio nal wave equations defined by fractal Laplacians
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The existence of the solution of the wave equation on graphs
The wave equation on a finite weighted graph does have a unique solution, but the paper's explicit solution formula is wrong and its infinite propagation speed theorem rests on an impossible eigenfunction assumption.