Cospectral Trees Indistinguishable by Scattering
Let v1 and v2 be two distinct vertices of an equilateral tree T0. Let ϕN(i) (i=1,2) be the characteristic functions of the Sturm-Liouville problem on T0 rooted at vi with Neumann conditions at the root and let ϕD(i) (i=1,2) be the characteristic functions of the Sturm-Liouville problem on T0 with Dirichlet conditions at the root. We prove that if attaching any tree to T0 at the vertices v1 and v2
