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  • The spectral gap for Laplace operators on metric graphs and the relation between the graph's edge connectivity is investigated, in particular what happens to the gap if an edge is added to (or deleted from) a graph. It is shown that, in contrast to discrete graphs, the connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding sufficiently large edges as well as cutting away sufficiently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given.
  • The spectral gap for Laplace operators on metric graphs and the relation between the graph's edge connectivity is investigated, in particular what happens to the gap if an edge is added to (or deleted from) a graph. It is shown that, in contrast to discrete graphs, the connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding sufficiently large edges as well as cutting away sufficiently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given. (en)
Title
  • Spectral gap for quantum graphs and their edge connectivity
  • Spectral gap for quantum graphs and their edge connectivity (en)
skos:prefLabel
  • Spectral gap for quantum graphs and their edge connectivity
  • Spectral gap for quantum graphs and their edge connectivity (en)
skos:notation
  • RIV/61389005:_____/13:00398984!RIV14-AV0-61389005
http://linked.open...avai/predkladatel
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  • I, P(GAP203/11/0701)
http://linked.open...iv/cisloPeriodika
  • 27
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  • 106983
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  • RIV/61389005:_____/13:00398984
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  • quantum graphs; geometric properties (en)
http://linked.open.../riv/klicoveSlovo
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [575F4B010781]
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  • Journal of Physics A-Mathematical and Theoretical
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  • 46
http://linked.open...iv/tvurceVysledku
  • Kurasov, P.
  • Malenová, Gabriela
  • Naboko, S.
http://linked.open...ain/vavai/riv/wos
  • 000320758400018
issn
  • 1751-8113
number of pages
http://bibframe.org/vocab/doi
  • 10.1088/1751-8113/46/27/275309
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