On the Laplacian Spectrum and Walk-regular Hypergraphs |
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Authors: | J A Rodrí guez |
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Institution: |
a Calle Juan Valera 197-207, 3 o 2 a Badalona 08914 Barcelona Spain. |
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Abstract: | We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on hypergraphs. For instance, we obtain upper bounds on the eccentricity and the excess of any vertex of hypergraphs. We extend to the case of hypergraphs the concepts of walk regularity and spectral regularity, showing that all walk-regular hypergraphs are spectrally-regular. Finally, we obtain an upper bound on the mean distance of walk-regular hypergraphs that involves all the Laplacian spectrum. |
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Keywords: | Laplacian Eigenvalues Walk-regular Hypergraphs Local Spectrum Excess Mean Distance Ams Subject Classifications: 05c50 05c65 05c12 05a20 15a42 |
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