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The α-spectral radius of general hypergraphs

Author

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  • Lin, Hongying
  • Zhou, Bo

Abstract

Given a hypergraph H of order n with rank k ≥ 2, denote by D(H) and A(H) the degree diagonal tensor and the adjacency tensor of H, respectively, of order k and dimension n. For real number α with 0 ≤ α < 1, the α-spectral radius of H is defined to be the spectral radius of the symmetric tensor αD(H)+(1−α)A(H). First, we establish a upper bound on the α-spectral radius of connected irregular hypergraphs. Then we propose three local transformations of hypergraphs that increase the α-spectral radius. We also identify the unique hypertree with the largest α-spectral radius and the unique hypergraph with the largest α-spectral radius among hypergraphs of given number of pendent edges, and discuss the unique hypertrees with the next largest α-spectral radius and the unicyclic hypergraphs with the largest α-spectral radius.

Suggested Citation

  • Lin, Hongying & Zhou, Bo, 2020. "The α-spectral radius of general hypergraphs," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304100
    DOI: 10.1016/j.amc.2020.125449
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    References listed on IDEAS

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    1. Honghai Li & Jia-Yu Shao & Liqun Qi, 2016. "The extremal spectral radii of $$k$$ k -uniform supertrees," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 741-764, October.
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