Rohleder, JonathanJonathanRohlederSeifert, ChristianChristianSeifert2019-11-202019-11-202017-11-01Integral Equations and Operator Theory 3 (89): 439-453 (2017-11-01)http://hdl.handle.net/11420/3824On an infinite, radial metric tree graph we consider the corresponding Laplacian equipped with self-adjoint vertex conditions from a large class including δ- and weighted δ′-couplings. Assuming the numbers of different edge lengths, branching numbers and different coupling conditions to be finite, we prove that the presence of absolutely continuous spectrum implies that the sequence of geometric data of the tree as well as the coupling conditions are eventually periodic. On the other hand, we provide examples of self-adjoint, non-periodic couplings which admit absolutely continuous spectrum.en0378-620X20173439453Absolutely continuous spectrumQuantum graphSchrödinger operatorTreeJournal Article10.1007/s00020-017-2388-4Other