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The Linear Unicyclic Hypergraph with the Second or Third Largest Spectral Radius

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Abstract

The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph. It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph, and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph. In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius, where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.

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Authors and Affiliations

  1. School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, P. R. China

    Chao Ding

  2. School of Mathematical Sciences, Anhui University, Hefei, 230601, P. R. China

    Chao Ding, Yi Zheng Fan & Jiang Chao Wan

Authors
  1. Chao Ding
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  2. Yi Zheng Fan
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  3. Jiang Chao Wan
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Corresponding author

Correspondence to Yi Zheng Fan.

Additional information

Supported by Natural Science Foundation of China (Grant Nos. 11871073, 11871077) and NSF of Department of Education of Anhui Province (Grant No. KJ2017A362)

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Ding, C., Fan, Y.Z. & Wan, J.C. The Linear Unicyclic Hypergraph with the Second or Third Largest Spectral Radius. Acta. Math. Sin.-English Ser. 36, 1140–1150 (2020). https://doi.org/10.1007/s10114-020-0089-4

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  • DOI: https://doi.org/10.1007/s10114-020-0089-4

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