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Spectral gap for quantum graphs and their edge connectivity
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 27, 275309- p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 46, no 27, 275309- p.
National Category
Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-92378DOI: 10.1088/1751-8113/46/27/275309ISI: 000320758400018OAI: oai:DiVA.org:su-92378DiVA: diva2:638686
Funder
Swedish Research Council, N50092501
Note

AuthorCount:3;

Available from: 2013-08-01 Created: 2013-08-01 Last updated: 2017-12-06Bibliographically approved

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