The Matching Polynomials and Spectral Radii of Uniform Supertrees

Li Su, Liying Kang, Honghai Li, Erfang Shan

Abstract


We study matching polynomials of uniform hypergraph and spectral radii of uniform supertrees. By comparing the matching polynomials of supertrees, we extend Li and Feng's results on grafting operations on graphs to supertrees. Using the methods of grafting operations on supertrees and comparing matching polynomials of supertrees, we determine the first $\lfloor\frac{d}{2}\rfloor+1$ largest spectral radii of $r$-uniform supertrees with size $m$ and diameter $d$. In addition, the first two smallest spectral radii of supertrees with size $m$ are determined.

Keywords


Hypergraph; Adjacency tensor; Eigenvalue; Matching polynomial; Supertree

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