Spectra of chains connected to complete graphs

Spectra of chains connected to complete graphs

We characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvectors of two types, eigenvectors that vanish exactly outside the complete graph and eigenvectors that decrease exponential...

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Veröffentlicht in:Linear algebra and its applications 2020-11, Vol.605, p.29-62
Hauptverfasser: Caputo, J.-G., Cruz-Pacheco, G., Knippel, A., Panayotaros, P.
Format: Artikel
Sprache:eng
Schlagworte:
Chains
Eigenvalues
Eigenvectors
Graph Laplacian
Graphs
Linear algebra
Protein model
Spectral graph theory
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Beschreibung
Zusammenfassung:We characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvectors of two types, eigenvectors that vanish exactly outside the complete graph and eigenvectors that decrease exponentially outside the complete graph. Our results also imply gaps between the eigenvalues corresponding to localized and extended eigenvectors.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.07.011