The signless Laplacian matrix of hypergraphs-Reference-Cited by-同舟云学术

The signless Laplacian matrix of hypergraphs

Published:2022-01-01 Issue:1 Volume:10 Page:327-342
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Cardoso Kauê¹,Trevisan Vilmar²

Affiliation:

1. Departamento de Ensino, Instituto Federal do Rio Grande do Sul - Campus Feliz, CEP 95770-000 , Feliz, RS , Brazil

2. Departamento de matemática Pura e Aplicada, Instituto de Matemática e Estatística, UFRGS, CEP 91509-900 , Porto Alegre, RS , Brazil

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2022-0166/pdf

Reference29 articles.

1. A. Banerjee, A. Char, and B. Mondal, Spectra of general hypergraphs, Linear Algebra Appl. 518 (2017), 14–30.

2. K. Feng, W. Ching, and W. Li, Spectra of hypergraphs and applications, J. Number Theory 60 (1996), 1–22.

3. N. Reff, Spectral properties of oriented hypergraphs, Electron. J. Linear Algebra 27 (2014), 373–391.

4. N. Reff and L. Rusnak, An oriented hypergraphic approach to algebraic graph theory, Linear Algebra Appl. 437 (2012), 2262–2270.

5. J. Rodriguez, On the Laplacian eigenvalues and metric parameters of hypergraphs, Linear Multilinear Algebra 50 (2002), 1–14.

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