Please use this identifier to cite or link to this item:
Title: Regular uniform hypergraphs, s-cycles, s-paths and their largest Laplacian H-eigenvalues
Authors: Qi, L 
Shao, JY
Wang, Q
Keywords: H-eigenvalue
Loose cycle
Loose path
Regular uniform hypergraph
Tight cycle
Tight path
Issue Date: 2014
Publisher: North-Holland
Source: Linear algebra and its applications, 2014, v. 443, p. 215-227 How to cite?
Journal: Linear algebra and its applications 
Abstract: In this paper, we show that the largest signless Laplacian H-eigenvalue of a connected k-uniform hypergraph G, where k≥3, reaches its upper bound 2Δ(G), where Δ(G) is the largest degree of G, if and only if G is regular. Thus the largest Laplacian H-eigenvalue of G, reaches the same upper bound, if and only if G is regular and odd-bipartite. We show that an s-cycle G, as a k-uniform hypergraph, where 1≤s≤k-1, is regular if and only if there is a positive integer q such that k=q(k-s). We show that an even-uniform s-path and an even-uniform non-regular s-cycle are always odd-bipartite. We prove that a regular s-cycle G with k=q(k-s) is odd-bipartite if and only if m is a multiple of 2t0, where m is the number of edges in G, and q=2t0(2 l0+1) for some integers t0 and l0. We identify the value of the largest signless Laplacian H-eigenvalue of an s-cycle G in all possible cases. When G is odd-bipartite, this is also its largest Laplacian H-eigenvalue. We introduce supervertices for hypergraphs, and show the components of a Laplacian H-eigenvector of an odd-uniform hypergraph are equal if such components correspond vertices in the same supervertex, and the corresponding Laplacian H-eigenvalue is not equal to the degree of the supervertex. Using this property, we show that the largest Laplacian H-eigenvalue of an odd-uniform generalized loose s-cycle G is equal to Δ(G)=2. We also show that the largest Laplacian H-eigenvalue of a k-uniform tight s-cycle G is not less than Δ(G)+1, if the number of vertices is even and k=4l+3 for some nonnegative integer l.
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2013.11.008
Appears in Collections:Journal/Magazine Article

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


Last Week
Last month
Citations as of Aug 11, 2017


Last Week
Last month
Citations as of Aug 15, 2017

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.