Abstract
In this paper we investigate the spectral and the scattering theory of Gauss–Bonnet operators acting on perturbed periodic combinatorial graphs. Two types of perturbation are considered: either a multiplication operator by a short-range or a long-range potential, or a short-range type modification of the graph. For short-range perturbations, existence and completeness of local wave operators are proved. In addition, similar results are provided for the Laplacian acting on edges.
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