Absolutely continuous spectrum for trees of finite forward cone type

We study a class of rooted trees which are not necessarily regular but exhibit a lot of symmetries. The spectrum of the corresponding graph Laplace operator is purely absolutely continuous and consists of finitely many intervals. Moreover for trees of the class which are not regular the absolutely continuous spectrum is stable under small perturbations by radially symmetric potentials. (This is joint work with Daniel Lenz and Simone Warzel.)