The eigenvectors to the p-spectral radius of general hypergraphs

Liying Kang (), Lele Liu () and Erfang Shan ()
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Liying Kang: Shanghai University
Lele Liu: Shanghai University
Erfang Shan: Shanghai University

Journal of Combinatorial Optimization, 2019, vol. 38, issue 2, No 12, 556-569

Abstract: Abstract Let $$\mathcal {A}$$ A be the adjacency tensor of a general hypergraph H. For any real number $$p\ge 1$$ p ≥ 1 , the p-spectral radius $$\lambda ^{(p)}(H)$$ λ ( p ) ( H ) of H is defined as $$\lambda ^{(p)}(H)=\max \{x^{\mathrm {T}}(\mathcal {A}x)\,|\,x\in {\mathbb {R}}^n, \Vert x\Vert _p=1\}$$ λ ( p ) ( H ) = max { x T ( A x ) | x ∈ R n , ‖ x ‖ p = 1 } . In this paper we present some bounds on entries of the nonnegative unit eigenvector corresponding to the p-spectral radius of H, which generalize the relevant results of uniform hypergraphs/graphs in the literature.

Keywords: Hypergraph; Adjacency tensor; p-spectral radius; 05C50; 05C65; 15A69 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-019-00393-2

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