Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/20864
Title: Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues
Authors: Hu, S
Qi, L 
Shao, JY
Issue Date: 2013
Source: Linear algebra and its applications, 2013, v. 439, no. 10, p. 2980-2998
Abstract: In this paper, we introduce the class of cored hypergraphs and power hypergraphs, and investigate the properties of their Laplacian H-eigenvalues. From an ordinary graph, one may generate a k-uniform hypergraph, called the kth power hypergraph of that graph. Power hypergraphs are cored hypergraphs, but not vice versa. Sunflowers, loose paths and loose cycles are power hypergraphs, while squids, generalized loose s-paths and loose s-cycles for 2≤s<k/2 are cored hypergraphs, but not power graphs in general. We show that the largest Laplacian H-eigenvalue of an even-uniform cored hypergraph is equal to its largest signless Laplacian H-eigenvalue. Especially, we find out these largest H-eigenvalues for even-uniform squids. Moreover, we show that the largest Laplacian H-eigenvalue of an odd-uniform squid, loose path and loose cycle is equal to the maximum degree, i.e., 2. We also compute the Laplacian H-spectra of the class of sunflowers. When k is odd, the Laplacian H-spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well.
Keywords: H-eigenvalue
Hypergraph
Laplacian
Power hypergraph
Tensor
Publisher: Elsevier
Journal: Linear algebra and its applications 
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2013.08.028
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