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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 05/2005

M.I.Belishev and A.F.Vakulenko
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INVERSE PROBLEMS ON GRAPHS:
RECOVERING THE TREE OF STRINGS BY THE BC-METHOD

This preprint was accepted March 18, 2005

ABSTRACT:
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 constitute the spectral data. The inverse problem
is to recover the structure of the graph and the densities from
the spectral data. If the graph doesn't contain cycles (is a tree),
it is determined by the spectral data up to a natural
isometry on the plane
(Belishev, 2004). In the paper this
uniqueness result is supplied with an efficient procedure of recovering
the tree. The numerical illustration is presented.

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