Operators and Matrices · Volume 14, Issue 3 Lower estimates on eigenvalues of quantum graphs 14-47 Pages 743-765 DOI 10.7153/oam-2020-14-47 Downloads Short PDF Full PDF PNG Authors Delio Mugnolo Marvin Plümer Keywords spectral geometry of quantum graphs planar graphs double cover conjecture normalized Laplacians Subject classes 34B45 05C50 35P15 81Q35