Title: Edge switching transformations of quantum graphs,
Abstract: Discussed here are the effects of basics graph transformations on the spectra
of associated quantum graphs. In particular it is shown that under an edge
switch the spectrum of the transformed Schrödinger operator is interlaced
with that of the original one. By implication, under edge swap the spectra
before and after the transformation, denoted by $\{ E_n\}_{n=1}^{\infty}$ and
$\{\widetilde E_n\}_{n=1}^{\infty}$ correspondingly, are level-2 interlaced, so
that $E_{n-2}\le \widetilde E_n\le E_{n+2}$. The proofs are guided by
considerations of the quantum graphs' discrete analogs.