  Spectral problems are considered generated by the Sturm-Liouville equation on
equilateral trees with the Dirichlet boundary conditions at the pendant
vertices and continuity and Kirchhoff's conditions at the interior vertices. It
is proved that there are no co-spectral (i.e., having the same spectrum of such
problem) among equilateral trees of less or equal 8 vertices. All co-spectral
trees of 9 vertices are presented.
