On Laplacian Energy of r-Uniform Hypergraphs

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum d...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 2; p. 382
Main Author Yalçın, N. Feyza
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2023
Subjects
Eigenvalues
Energy
graph energy
Graph theory
Graphs
hypergraph
Laplacian matrix
Matrix representation
Symmetry
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Summary:The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum degree, and the first Zagreb index for the greatest Laplacian eigenvalue and Laplacian energy of r-uniform hypergraphs and r-uniform regular hypergraphs. As a result of these bounds, Nordhaus–Gaddum type bounds are obtained for the Laplacian energy.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15020382