TY - JOUR
AU - Warzel, Simone
AB - 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.
TI - Edge switching transformations of quantum graphs
JF - Mathematics
DO - 10.12693/APhysPolA.132.1699
DA - 2017-10-22
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/edge-switching-transformations-of-quantum-graphs-G7oAiDTct7
VL - 2022
IS - 1710
DP - DeepDyve
ER -