A Laplacian eigenbasis for threshold graphs
Let GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-10-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2024-0029 |
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| _version_ | 1850257208358469632 |
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| author | Macharete Rafael R. Del-Vecchio Renata R. Teixeira Heber de Lima Leonardo |
| author_facet | Macharete Rafael R. Del-Vecchio Renata R. Teixeira Heber de Lima Leonardo |
| author_sort | Macharete Rafael R. |
| collection | DOAJ |
| description | Let GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs that are weakly Hadamard diagonalizable. |
| format | Article |
| id | doaj-art-e40bed5346cc416b8b7df103e6bf4592 |
| institution | OA Journals |
| issn | 2300-7451 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj-art-e40bed5346cc416b8b7df103e6bf45922025-08-20T01:56:28ZengDe GruyterSpecial Matrices2300-74512024-10-011218611910.1515/spma-2024-0029A Laplacian eigenbasis for threshold graphsMacharete Rafael R.0Del-Vecchio Renata R.1Teixeira Heber2de Lima Leonardo3Programa de Pós-Graduação em Matemática, Universidade Federal Fluminense, Niterói, 24210-201, BrazilPrograma de Pós-Graduação em Matemática, Universidade Federal Fluminense, Niterói, 24210-201, BrazilPrograma de Pós-Graduação em Matemática, Universidade Federal do Paraná, Paraná, 81530-015, BrazilPrograma de Pós-Graduação em Matemática, Universidade Federal do Paraná, Paraná, 81530-015, BrazilLet GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs that are weakly Hadamard diagonalizable.https://doi.org/10.1515/spma-2024-0029threshold graphspectral characterizationlaplacian matrixweakly hadamard diagonalizable graph05c5005c35 |
| spellingShingle | Macharete Rafael R. Del-Vecchio Renata R. Teixeira Heber de Lima Leonardo A Laplacian eigenbasis for threshold graphs Special Matrices threshold graph spectral characterization laplacian matrix weakly hadamard diagonalizable graph 05c50 05c35 |
| title | A Laplacian eigenbasis for threshold graphs |
| title_full | A Laplacian eigenbasis for threshold graphs |
| title_fullStr | A Laplacian eigenbasis for threshold graphs |
| title_full_unstemmed | A Laplacian eigenbasis for threshold graphs |
| title_short | A Laplacian eigenbasis for threshold graphs |
| title_sort | laplacian eigenbasis for threshold graphs |
| topic | threshold graph spectral characterization laplacian matrix weakly hadamard diagonalizable graph 05c50 05c35 |
| url | https://doi.org/10.1515/spma-2024-0029 |
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