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The eigenvectors to the p-spectral radius of general hypergraphs

Author

Listed:
  • Liying Kang

    (Shanghai University)

  • Lele Liu

    (Shanghai University)

  • Erfang Shan

    (Shanghai University
    Shanghai University)

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.

Suggested Citation

  • Liying Kang & Lele Liu & Erfang Shan, 2019. "The eigenvectors to the p-spectral radius of general hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 556-569, August.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:2:d:10.1007_s10878-019-00393-2
    DOI: 10.1007/s10878-019-00393-2
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    References listed on IDEAS

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    1. Yuejian Peng & Qingsong Tang & Cheng Zhao, 2015. "On Lagrangians of r-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 812-825, October.
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    Cited by:

    1. Jing Wang & Liying Kang & Erfang Shan, 0. "The principal eigenvector to $$\alpha $$α-spectral radius of hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-18.
    2. Jing Wang & Liying Kang & Erfang Shan, 2021. "The principal eigenvector to $$\alpha $$ α -spectral radius of hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 42(2), pages 258-275, August.

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