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The Maximum α-spectral Radius of Unicyclic Hypergraphs with Fixed Diameter

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Abstract

For 0 ≤ α < 1, the α-spectral radius of an r-uniform hypergraph G is the spectral radius of \({{\cal A}_\alpha}(G) = \alpha {\cal D}(G) + (1 - \alpha){\cal A}(G)\), where \({\cal D}(G)\) and \({\cal A}(G)\) are the diagonal tensor of degrees and adjacency tensor of G, respectively. In this paper, we show the perturbation of α-spectral radius by contracting an edge. Then we determine the unique unicyclic hypergraph with the maximum α-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter. We also determine the unique unicyclic hypergraph with the maximum α-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Li Ying Kang & Jing Wang

  2. School of Management, Shanghai University, Shanghai, 200444, P. R. China

    Er Fang Shan

Authors
  1. Li Ying Kang
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  2. Jing Wang
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  3. Er Fang Shan
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Correspondence to Er Fang Shan.

Additional information

Supported by the National Nature Science Foundation of China (Grant Nos. 11871329, 11971298)

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Kang, L.Y., Wang, J. & Shan, E.F. The Maximum α-spectral Radius of Unicyclic Hypergraphs with Fixed Diameter. Acta. Math. Sin.-English Ser. 38, 924–936 (2022). https://doi.org/10.1007/s10114-022-0611-y

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  • DOI: https://doi.org/10.1007/s10114-022-0611-y

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