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math.SP2022
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…
math.SP2022★ 2 cited
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…