Abstract
Lower and upper estimates for the spectral of the Laplacian on a compact metric graph are discussed. New upper estimates are presented and existing lower estimates are reviewed. The accuracy of these estimates is checked in the case of complete (not necessarily regular) graph with large number of vertices.
The author was supported in part by Swedish Research Council Grant #50092501.
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Acknowledgements
The author would like to thank Delio Mugnolo for organizing an extremely stimulating conference in Bielefeld. Many thanks go to Olaf Post for discussions concerning Cheeger estimate (4), which was proved by Rune Suhr [8]. The author is grateful to anonymous referee for correcting inaccuracies and fruitful remarks.
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Kurasov, P. (2015). Spectral Gap for Complete Graphs: Upper and Lower Estimates. In: Mugnolo, D. (eds) Mathematical Technology of Networks. Springer Proceedings in Mathematics & Statistics, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-319-16619-3_8
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DOI: https://doi.org/10.1007/978-3-319-16619-3_8
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