Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/35791
Title: H+-Eigenvalues of Laplacian and signless Laplacian tensors
Authors: Qi, LQ 
Keywords: Laplacian tensor
Signless Laplacian tensor
Uniform hypergraph
H+-eigenvalue
Issue Date: 2014
Publisher: International Press
Source: Communications in mathematical sciences, 2014, v. 12, no. 6, p. 1045-1064 How to cite?
Journal: Communications in mathematical sciences 
Abstract: We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H+-eigenvalues, i.e., H-eigenvalues with non-negative H-eigenvectors, and H++-eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H++-eigenvalue, but has several other H+-eigenvalues. We identify their largest and smallest H+-eigenvalues, and establish some maximum and minimum properties of these H+-eigenvalues. We then define analytic connectivity of a uniform hypergraph and discuss its application in edge connectivity.
URI: http://hdl.handle.net/10397/35791
ISSN: 1539-6746 (print)
1945-0796 (online)
DOI: 10.4310/CMS.2014.v12.n6.a3
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