65 citations · 324 across the 16 of their papers we have counts for
18 papers
Spectrally grown graphs
Mats-Erik Pistol, Pavel Kurasov
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary con…
Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap
Gregory Berkolaiko, James B. Kennedy, Pavel Kurasov +1
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based…
Always detectable eigenfunctions on metric graphs
Pavel Kurasov
It is proven following [18[ that Laplacians with standard vertex continuous on metric trees and with standard and Dirichlet conditions on arbitrary metric graphs possess an infinit…
On isospectral metric graphs
Pavel Kurasov, Jacob Muller
A new class of isospectral graphs is presented. These graphs are isospectral with respect to both the normalised Laplacian on the discrete graph and the standard differential Lapla…
Hearing Euler characteristic of graphs
Michał Ławniczak, Pavel Kurasov, Szymon Bauch +3
The Euler characteristic and the total length are the most important topological and geometrical characteristics of a metric graph. Here, and …
A theory of spectral partitions of metric graphs
James B. Kennedy, Pavel Kurasov, Corentin Léna +1
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus…