The signless Laplacian matrix of hypergraphs
In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph such as the maximum degree, diameter, and the ch...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-05-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2022-0166 |
| _version_ | 1818018013026189312 |
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| author | Cardoso Kauê Trevisan Vilmar |
| author_facet | Cardoso Kauê Trevisan Vilmar |
| author_sort | Cardoso Kauê |
| collection | DOAJ |
| description | In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph such as the maximum degree, diameter, and the chromatic number. In addition, we characterize the complete signless Laplacian spectrum for the class of power hypergraphs from the spectrum of its base hypergraph. |
| first_indexed | 2024-04-14T07:34:35Z |
| format | Article |
| id | doaj.art-224db9d1869245a9bf70f9f58533629a |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-04-14T07:34:35Z |
| publishDate | 2022-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-224db9d1869245a9bf70f9f58533629a2022-12-22T02:05:43ZengDe GruyterSpecial Matrices2300-74512022-05-0110132734210.1515/spma-2022-0166The signless Laplacian matrix of hypergraphsCardoso Kauê0Trevisan Vilmar1Departamento de Ensino, Instituto Federal do Rio Grande do Sul - Campus Feliz, CEP 95770-000, Feliz, RS, BrazilDepartamento de matemática Pura e Aplicada, Instituto de Matemática e Estatística, UFRGS, CEP 91509-900, Porto Alegre, RS, BrazilIn this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph such as the maximum degree, diameter, and the chromatic number. In addition, we characterize the complete signless Laplacian spectrum for the class of power hypergraphs from the spectrum of its base hypergraph.https://doi.org/10.1515/spma-2022-0166hypergraphsignless laplacianspectral radiuspower hypergraph05c6505c5015a18 |
| spellingShingle | Cardoso Kauê Trevisan Vilmar The signless Laplacian matrix of hypergraphs Special Matrices hypergraph signless laplacian spectral radius power hypergraph 05c65 05c50 15a18 |
| title | The signless Laplacian matrix of hypergraphs |
| title_full | The signless Laplacian matrix of hypergraphs |
| title_fullStr | The signless Laplacian matrix of hypergraphs |
| title_full_unstemmed | The signless Laplacian matrix of hypergraphs |
| title_short | The signless Laplacian matrix of hypergraphs |
| title_sort | signless laplacian matrix of hypergraphs |
| topic | hypergraph signless laplacian spectral radius power hypergraph 05c65 05c50 15a18 |
| url | https://doi.org/10.1515/spma-2022-0166 |
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