Eigenvalue estimates on quantum graphs
Spectral Theory
2016-09-26 v1 Mathematical Physics
math.MP
Abstract
On a finite connected metric graph, we establish upper bounds for the eigenvalues of the Laplacian. These bounds depend on the length, the Betti number, and the number of pendant vertices. For trees, these estimates are sharp. We also establish sharp upper bounds for the spectral gap of the complete graph . The proofs are based on estimates for eigenvalues on graphs with Dirichlet conditions imposed at the pendant vertices.
Cite
@article{arxiv.1609.07471,
title = {Eigenvalue estimates on quantum graphs},
author = {Sinan Ariturk},
journal= {arXiv preprint arXiv:1609.07471},
year = {2016}
}