Uniform supertrees with extremal spectral radii

doi:10.1007/s11464-020-0873-6

Front. Math. China

2020, Vol. 15

Issue (6) : 1211-1229 https://doi.org/10.1007/s11464-020-0873-6

RESEARCH ARTICLE

Uniform supertrees with extremal spectral radii

Wen-Huan WANG(

), Ling YUAN

Department of Mathematics, Shanghai University, Shanghai 200444, China

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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.

Keywords Hypergraph spectral radius supertree matching polynomial

Corresponding Author(s): Wen-Huan WANG

Issue Date: 05 February 2021

Cite this article:

Wen-Huan WANG,Ling YUAN. Uniform supertrees with extremal spectral radii[J]. Front. Math. China, 2020, 15(6): 1211-1229.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0873-6
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I6/1211

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