Please use this identifier to cite or link to this item:
Title: Spectral directed hypergraph theory via tensors
Authors: Xie, J
Qi, LQ 
Keywords: Spectrum
Directed hypergraph
Adjacency tensor
Laplacian tensor
Signless Laplacian tensor
Issue Date: 2016
Publisher: Taylor & Francis
Source: Linear and multilinear algebra, 2016, v. 64, no. 4, p. 780-794 How to cite?
Journal: Linear and multilinear algebra 
Abstract: In this paper, we show that each of the adjacency tensor, the Laplacian tensor and the signless Laplacian tensor of a uniform directed hypergraph has n linearly independent H-eigenvectors. Some lower and upper bounds for the largest and smallest adjacency, Laplacian and signless Laplacian H-eigenvalues of a uniform directed hypergraph are given. For a uniform directed hypergraph, the smallest Laplacian H-eigenvalue is 0. On the other hand, the upper bound of the largest adjacency and signless Laplacian H-eigenvalues are achieved if and only if it is a complete directed hypergraph. For a uniform directed hyperstar, all adjacency H-eigenvalues are 0. At the same time, we make some conjectures about the nonnegativity of one H-eigenvector corresponding to the largest H-eigenvalue, and raise some questions about whether the Laplacian and signless Laplacian tensors are positive semi-definite for a uniform directed hypergraph.
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2015.1125838
Appears in Collections:Journal/Magazine Article

View full-text via PolyU eLinks SFX Query
Show full item record

Page view(s)

Last Week
Last month
Checked on Aug 14, 2017

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.