Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph Academic Article uri icon


  • 2016 Elsevier Inc. We prove that after an arbitrarily small adjustment of edge lengths, the spectrum of a compact quantum graph with -type vertex conditions can be simple. We also show that the eigenfunctions, with the exception of those living entirely on a looping edge, can be made to be non-vanishing on all vertices of the graph. As an application of the above result, we establish that the secular manifold (also called determinant manifold) of a large family of graphs has exactly two smooth connected components.

published proceedings

  • Journal of Mathematical Analysis and Applications

author list (cited authors)

  • Berkolaiko, G., & Liu, W.

citation count

  • 19

complete list of authors

  • Berkolaiko, Gregory||Liu, Wen

publication date

  • January 2017