An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Quantum graphs and topology

Author: Pavel Kurasov (Lund University )

Abstract

Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues. This result is generalized for Schr\"odinger operators on metric graphs.