A remark on the absence of eigenvalues in continuous spectra for discrete Schr\'{o}dinger operators on periodic lattices

We prove a Rellich-Vekua type theorem for Schr\"{o}dinger operators with exponentially decreasing potentials on a class of lattices containing square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation theorem and the non-existence of eigenvalues embedded in the continuous spectrum.