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Uniform supertrees with extremal spectral radii

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Abstract

A supertree is a connected and acyclic hypergraph. We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees. First, by using the matching polynomials of supertrees, a new and useful grafting operation is proposed for comparing the spectral radii of supertrees, and its applications are shown to obtain the supertrees with the extremal spectral radii among some kinds of r-uniform supertrees. Second, the supertree with the third smallest spectral radius among the r-uniform supertrees is deduced. Third, among the r-uniform supertrees with a given maximum degree, the supertree with the smallest spectral radius is derived. At last, among the r-uniform starlike supertrees, the supertrees with the smallest and the largest spectral radii are characterized.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871040, 11001166).

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Authors and Affiliations

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

    Wen-Huan Wang & Ling Yuan

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  1. Wen-Huan Wang
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  2. Ling Yuan
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Correspondence to Wen-Huan Wang.

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Wang, WH., Yuan, L. Uniform supertrees with extremal spectral radii. Front. Math. China 15, 1211–1229 (2020). https://doi.org/10.1007/s11464-020-0873-6

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  • DOI: https://doi.org/10.1007/s11464-020-0873-6

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