Sharp Bounds for the Signless Laplacian Spectral Radius of Uniform Hypergraphs

Let H be a k -uniform hypergraph on n vertices with degree sequence Δ = d 1 ≥ ⋯ ≥ d n = δ . E i denotes the set of edges of H containing i . The average 2-degree of vertex i of H is m i = ∑ { i , i 2 , … i k } ∈ E i d i 2 … d i k / d i k - 1 . In this paper, in terms of m i and d i , we give some up...

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Bibliographic Details
Published in:Bulletin of the Iranian Mathematical Society 2019-04, Vol.45 (2), p.583-591
Main Authors: He, Jun, Liu, Yan-Min, Tian, Jun-Kang, Liu, Xiang-Hu
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Paper
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Summary:Let H be a k -uniform hypergraph on n vertices with degree sequence Δ = d 1 ≥ ⋯ ≥ d n = δ . E i denotes the set of edges of H containing i . The average 2-degree of vertex i of H is m i = ∑ { i , i 2 , … i k } ∈ E i d i 2 … d i k / d i k - 1 . In this paper, in terms of m i and d i , we give some upper bounds and lower bounds for the spectral radius of the signless Laplacian tensor ( Q ( H ) ) of H . Some examples are given to show the tightness of these bounds.
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-018-0150-6