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In this paper we study Schrödinger operators with absolutely integrable potentials on metric graphs. Uniform bounds—i.e. depending only on the graph and the potential—on the difference between the $$n^\mathrm{th}$$ nth eigenvalues of the Laplace and Schrödinger operators are obtained. This in turn allows us to prove an extension of the classical Ambartsumian Theorem which was originally proven for...
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