Solution of scaling quantum networks

We show that all scaling quantum graphs are explicitly integrable, i.e. any one of their spectral eigenvalues $E_n$ is computable analytically, explicitly, and individually for any given $n$. This is surprising, since quantum graphs are excellent models of quantum chaos [see, e.g., T. Kottos and H. Schanz, Physica E {\bf 9}, 523 (2001)].