Parter Vertices and Generalization of the Downer Branch Mechanism in the General Setting
Parter Vertices and Generalization of the Downer Branch Mechanism in the General Setting
复制标题
一般环境下下分支机制的伙伴顶点和推广
DOI：
10.1080/03081087.2023.2176414
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发表时间：
2023
影响因子：
1.1
通讯作者：
Charles R. Johnson
中科院分区：
文献类型：
--
作者：
Kenji Toyonaga;Charles R. Johnson
域上的方阵的图形中的顶点可以根据它们的去除如何改变所识别的特征值的几何多重性来分类。有三种可能性：（Parter）;没有变化（neutral）;（dower）。当图是树时，“下行分支机制”区分Parter顶点。在这里，我们发现这种机制如何推广到一般图，无论是埃尔米特矩阵还是一般矩阵。然后，我们应用这些新的思想，对一般图中的悬垂边进行分类，并理解当存在2-downner边时，一般图中2-downner边圈的存在性。这进一步解释了为什么这样的边缘不能出现在树中。
Vertices in the graph of a square matrix over a field may be classified as to how their removal changes the geometric multiplicity of an identified eigenvalue. There are three possibilities:(Parter); no change (neutral); and(downer). When the graph is a tree, the ‘downer branch mechanism’ distinguishes the Parter vertices. Here, we discover how this mechanism generalizes for general graphs, both for Hermitian matrices and general matrices. Then, we apply the new ideas, both to classify pendent edges in general graphs, and to understand the existence of 2-downer edge cycles in general graphs, when there is a 2-downer edge. This is a further explanation of why such edges cannot occur in trees.