Exner, PavelPavelExnerSeifert, ChristianChristianSeifertStollmann, PeterPeterStollmann2021-07-232021-07-232013-07-12Annales Henri Poincare 15 (6): 1109-1121 (2014)http://hdl.handle.net/11420/9949In this paper, we prove that the existence of absolutely continuous spectrum of the Kirchhoff Laplacian on a radial metric tree graph together with a finite complexity of the geometry of the tree implies that the tree is in fact eventually periodic. This complements the results by Breuer and Frank in (Rev Math Phys 21(7):929-945, 2009) in the discrete case as well as for sparse trees in the metric case. © 2013 Springer Basel.en1424-06612013611091121Springer International Publishing AGMathematikJournal Article10.1007/s00023-013-0274-4Other