Abstract
We propose a simple method for resolution of cospectrality of Schrödinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the S-functions of the corresponding scattering problems on these (non-compact) graphs. We show that in several cases—including general graphs on at most six vertices, general trees on at most nine vertices, and general fuzzy balls—eigenvalues and scattering data are together sufficient to distinguish cospectral metric graphs.
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