37 citations · 81 across the 8 of their papers we have counts for
9 papers
On the interplay between embedded graphs and delta-matroids
Carolyn Chun, Iain Moffatt, Steven D. Noble +1
The mutually enriching relationship between graphs and matroids has motivated discoveries in both fields. In this paper, we exploit the similar relationship between embedded graphs…
Heat-kernel and resolvent asymptotics for Schroedinger operators on metric graphs
Jens Bolte, Sebastian Egger, Ralf Rueckriemen
We consider Schroedinger operators on compact and non-compact (finite) metric graphs. For such operators we analyse their spectra, prove that their resolvents can be represented as…
Matroids, Delta-matroids and Embedded Graphs
Carolyn Chun, Iain Moffatt, Steven D. Noble +1
Matroid theory is often thought of as a generalization of graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show tha…
Heat trace asymptotics for quantum graphs
Ralf Rueckriemen
We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admi…
Trace Formulae for quantum graphs with edge potentials
Ralf Rueckriemen, Uzy Smilansky
This work explores the spectra of quantum graphs where the Schrödinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced…
Quasi-isospectrality on quantum graphs
Ralf Rueckriemen
Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere asi…
Quantum graphs and their spectra
Ralf Rueckriemen
We show that families of leafless quantum graphs that are isospectral for the standard Laplacian are finite. We show that the minimum edge length is a spectral invariant. We give a…
Isospectral Metrics on Projective Spaces
Ralf Rueckriemen
We construct isospectral non isometric metrics on real and complex projective space. We recall the construction using isometric torus actions by Carolyn Gordon in chapter 2. In cha…
Recovering quantum graphs from their Bloch spectrum
Ralf Rueckriemen
We define the Bloch spectrum of a quantum graph to be the collection of the spectra of a family of Schrodinger operators parametrized by the cohomology of the quantum graph. We sho…