Uniform supertrees with extremal spectral radii

被引：5

作者：

Wang, Wen-Huan ^{[1
]}

Yuan, Ling ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2020年 / 15卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Hypergraph; spectral radius; supertree; matching polynomial; HYPERGRAPHS; EIGENVALUES; BOUNDS; 1ST;

D O I：

10.1007/s11464-020-0873-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1211 / 1229

页数：19

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