Steklov Institute of Mathematics at St.Petersburg

PREPRINT 05/2005


M.I.Belishev and A.F.Vakulenko

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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