The inverse scattering problem for metric graphs and the traveling salesman problem

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dc.creatorKostrykin, Vadim
dc.creatorSchrader, Robert
dc.date2006-03-02
dc.date.accessioned2026-07-07T07:06:18Z
dc.date.available2026-07-07T07:06:18Z
dc.descriptionWe present a solution to the inverse scattering problem for differential Laplace operators on metric noncompact graphs. We prove that for almost all boundary conditions (i) the scattering matrix uniquely determines the graph and its metric structure, (ii) the boundary conditions are determined uniquely up to trivial gauge transformations. The main ingredient of our approach is a combinatorial Fourier expansion of the scattering matrix which encodes the topology of the graph into analytic properties of the scattering matrix. Using the technique developed in this work, we also propose an analytic approach to solving some combinatorial problems on graphs, in particular, the Traveling Salesman Problem.
dc.identifierhttps://arxiv.org/abs/math-ph/0603010
dc.identifierhttp://arxiv.org/abs/math-ph/0603010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109975
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subject34B45; 05C35; 47A40
dc.titleThe inverse scattering problem for metric graphs and the traveling salesman problem
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