17 citations · 44 across the 6 of their papers we have counts for
6 papers
Spectral Determinants of Almost Equilateral Quantum Graphs
Jonathan Harrison, Tracy Weyand
Kirchoff's matrix tree theorem of 1847 connects the number of spanning trees of a graph to the spectral determinant of the discrete Laplacian [22]. Recently an analogue was obtaine…
Can One Hear the Spanning Trees of a Quantum Graph?
Jonathan Harrison, Tracy Weyand
Kirchhoff showed that the number of spanning trees of a graph is the spectral determinant of the combinatorial Laplacian divided by the number of vertices; we reframe this result i…
Relating Zeta Functions of Discrete and Quantum Graphs
Jonathan Harrison, Tracy Weyand
We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the correspo…
Zeta Functions of the Dirac Operator on Quantum Graphs
J. M. Harrison, T. Weyand, K. Kirsten
We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The t…
Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs
Ram Band, Gregory Berkolaiko, Tracy Weyand
We study the nodal count of the so-called bi-dendral graphs and show that it exhibits an anomaly: the nodal surplus is never equal to 0 or , the first Betti number of the graph.…
Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions
G. Berkolaiko, T. Weyand
We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the -th eigenfunction of the Schrödinger operator on a quantum graph is related…