Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/62498
Title: Spectral directed hypergraph theory via tensors
Authors: Xie, J
Qi, LQ 
Keywords: Spectrum
Directed hypergraph
H-eigenvalue
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.
URI: http://hdl.handle.net/10397/62498
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2015.1125838
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