Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue

被引：4

作者：

Toyonaga, Kenji ^{[1
]}

Johnson, Charles R. ^{[2
]}

机构：

[1] Natl Inst Technol, Kitakyushu Coll, Dept Creat Engn, Kitakyushu, Fukuoka, Japan

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA

来源：

LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 10期

关键词：

Edge; eigenvalues; graph; Hermitian matrix; multiplicity;

D O I：

10.1080/03081087.2020.1825606

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the change in the multiplicities of an eigenvalue of an Hermitian matrix whose graph is a general undirected graph, when an edge is removed from the graph. The same question when the graph is a tree has been investigated in prior work. Here, we give possible classifications of edges in a general graph in terms of the statuses of adjacent vertices. It turns out that there are four cases that do occur in a general graph but cannot occur in a tree.

引用

页码：1803 / 1812

页数：10

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