### Abstract

The uniqueness question for the inverse problem for a Schr\"odinger equation on a compact interval was answered by theorems due to Borg, Levinson, and Marchenko for various sets of data (two spectra, one spectrum and boundary data of eigenfunctions, and one spectrum and norming constants of eigenfunctions, respectively). These theorems have generalizations to finite trees which will be presented and discussed.

This is joint work with Malcolm Brown, Cardiff.