# Boundary spectral inverse problem on a class of graphs (trees) by the BC method

@article{Belishev2004BoundarySI, title={Boundary spectral inverse problem on a class of graphs (trees) by the BC method}, author={Mikhail I. Belishev}, journal={Inverse Problems}, year={2004}, volume={20}, pages={647-672} }

A planar graph consisting of strings of variable densities is considered. The spectrum of the Dirichlet problem on the graph and the values of derivatives of the (normalized) eigenfunctions at the boundary vertices form the spectral data. We show that the graph without cycles (tree) and the densities of its edges are determined by the spectral data uniquely up to a natural isometry in the plane. In the framework of our approach (boundary control method; Belishev 1986) we study the boundary…

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