Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/36130
Title: The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph
Authors: Hu, SL
Qi, LQ 
Xie, JS
Keywords: Hypergraph
Laplacian
Signless Laplacian
Tensor
H-eigenvalue
Issue Date: 2015
Publisher: North-Holland
Source: Linear algebra and its applications, 2015, v. 469, p. 1-27 How to cite?
Journal: Linear algebra and its applications 
Abstract: In this paper, we show that the largest Laplacian H-eigenvalue of a k-uniform nontrivial hypergraph is strictly larger than the maximum degree when k is even. A tight lower bound for this eigenvalue is given. For a connected even-uniform hypergraph, this lower bound is achieved if and only if it is a hyperstar. However, when k is odd, in certain cases the largest Laplacian H-eigenvalue is equal to the maximum degree, which is a tight lower bound. On the other hand, tight upper and lower bounds for the largest signless Laplacian H-eigenvalue of a k-uniform connected hypergraph are given. For connected k-uniform hypergraphs of fixed number of vertices (respectively fixed maximum degree), the upper (respectively lower) bound of their largest signless Laplacian H-eigenvalues is achieved exactly for the complete hypergraph (respectively the hyperstar). The largest Laplacian H-eigenvalue is always less than or equal to the largest signless Laplacian H-eigenvalue. When the hypergraph is connected, the equality holds here if and only if k is even and the hypergraph is odd-bipartite.
URI: http://hdl.handle.net/10397/36130
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2014.11.020
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