Spectral radii of two kinds of uniform hypergraphs

Liying Kang, Lele Liu, Liqun Qi and Xiying Yuan

Applied Mathematics and Computation, 2018, vol. 338, issue C, 661-668

Abstract: Let A(H) be the adjacency tensor (hypermatrix) of uniform hypergraph H. The maximum modulus of the eigenvalues of A(H) is called the spectral radius of H, denoted by ρ(H). In this paper, a conjecture concerning the spectral radii of linear bicyclic uniform hypergraphs is solved, with these results the hypergraph with the largest spectral radius is completely determined among the linear bicyclic uniform hypergraphs. For a t-uniform hypergraph G its generalized power r-uniform hypergraph Gr, s is defined in this paper. An exact relation between ρ(G) and ρ(Gr, s) is proved, more precisely ρ(Gr,s)=(ρ(G))tsr.

Keywords: Uniform hypergraph; Adjacency tensor; Spectral radius; Linear bicyclic hypergraph; Generalized power uniform hypergraph (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:661-668

DOI: 10.1016/j.amc.2018.06.015

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