On the spectrum of the Laplacian on regular metric trees

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Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “One can find discussion of infinite graphs in [47, 75, 145, 150, 180, 204, 205], as well as in Section 7.”
Harmonic Analysis on Metrized Graphs (2004, background): “ So it remains to prove that fn converges pointwise to f.”
Quantum graphs: I. Some basic structures (2004, background): “references therein), the corresponding theory of quantum graphs is just developing (e.g., examples of such studies in [3, 5, 6, 7, 8, 9, 15], [16] - [20], [25], [29] - [35], [39], [43] - [49], [56] - [58], [64, 65, 70, 74, 79 , 80] and further references in [54]).”
Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs (2004, background): “at point spectrum can arise for diﬀerent reasons on graphs that are not periodic, e.g. on trees. For instance, one can have bound states on inﬁnite trees with suﬃciently fast growing branching number [43]. We will consider an inﬁnite combinatorial or quantum graph Γ with a faithful co-compact action”