Spectra of chains connected to complete graphs
| Autor: | Gustavo Cruz-Pacheco, Arnaud Knippel, Panayotis Panayotaros, J. G. Caputo |
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| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory 010102 general mathematics Spectrum (functional analysis) MathematicsofComputing_GENERAL MathematicsofComputing_NUMERICALANALYSIS Complete graph 010103 numerical & computational mathematics 01 natural sciences Spectral line Mathematics - Spectral Theory Combinatorics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Geometry and Topology 0101 mathematics Spectral Theory (math.SP) Laplace operator Eigenvalues and eigenvectors MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | Linear Algebra and its Applications. 605:29-62 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2020.07.011 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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