The change in multiplicity of an eigenvalue due to adding or removing edges
The change in multiplicity of an eigenvalue due to adding or removing edges
复制标题
由于添加或删除边而导致的特征值重数的变化
DOI：
10.1016/j.laa.2018.09.017
复制
发表时间：
2019
影响因子：
1.1
通讯作者：
K. Toyonaga
中科院分区：
文献类型：
--
作者：
Charles R. Johnson;Carlos M. Saiago;K. Toyonaga
本文研究了具有简单图G的Hermitian矩阵的特征值重数在边插入G或从G中移除时的变化。我们专注于的情况下，多重特征值不改变，由于插入或删除边事件的顶点。此外，我们展示了当两个不相交的图与一个边连接时，特征值的多重性的变化是如何发生的，基于连接的顶点的状态。最后，我们给出了图中割边的可能分类，并刻画了每种可能状态的出现。
We investigate the change in the multiplicities of the eigenvalues of a Hermitian matrix with a simple graphG, when edges are inserted intoGor removed fromG. We focus upon cases in which the multiplicity of the eigenvalue does not change due to inserting or removing edges incident to a vertex. Furthermore, we show how the change in the multiplicities of the eigenvalues occur, when two disjoint graphs are connected with one edge, based upon the status of the vertices that are connected. Lastly, we give the possible classifications of cut-edges in a graph and characterize the occurrence of each possible status.