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author = {Evans M. Harrell II and James B. Kennedy and Gabriel J. Ramos},
title = {Bounds on eigenvalue ratios of quantum graph Laplacians},
journal = {arXiv preprint arXiv:2603.26172},
year = {2026},
note = {Current manuscript date: 24 August 2026}
}
@article{BerkolaikoKennedyKurasovMugnolo2017,
author = {Gregory Berkolaiko and James B. Kennedy and Pavel Kurasov and Delio Mugnolo},
title = {Edge connectivity and the spectral gap of combinatorial and quantum graphs},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {50},
pages = {365201},
year = {2017}
}
@article{BerkolaikoKennedyKurasovMugnolo2019,
author = {Gregory Berkolaiko and James B. Kennedy and Pavel Kurasov and Delio Mugnolo},
title = {Surgery principles for the spectral analysis of quantum graphs},
journal = {Transactions of the American Mathematical Society},
volume = {372},
pages = {5153--5197},
year = {2019}
}
@article{BerkolaikoLatushkinSukhtaiev2019,
author = {Gregory Berkolaiko and Yuri Latushkin and Selim Sukhtaiev},
title = {Limits of quantum graph operators with shrinking edges},
journal = {Advances in Mathematics},
volume = {352},
pages = {632--669},
year = {2019}
}
@book{BerkolaikoKuchment2013,
author = {Gregory Berkolaiko and Peter Kuchment},
title = {Introduction to Quantum Graphs},
series = {Mathematical Surveys and Monographs},
volume = {186},
publisher = {American Mathematical Society},
year = {2013}
}
@article{Friedlander2005,
author = {Leonid Friedlander},
title = {Genericity of simple eigenvalues for a metric graph},
journal = {Israel Journal of Mathematics},
volume = {146},
pages = {149--156},
year = {2005}
}
@article{Nicaise1987,
author = {Serge Nicaise},
title = {Spectre des reseaux topologiques finis},
journal = {Bulletin des Sciences Mathematiques, IIe Serie},
volume = {111},
pages = {401--413},
year = {1987}
}
@book{Kurasov2024,
author = {Pavel Kurasov},
title = {Spectral Geometry of Graphs},
series = {Operator Theory: Advances and Applications},
volume = {293},
publisher = {Birkhauser},
year = {2024}
}
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