ABSTRACT

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.

中文翻译：

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与特征值的多重性变化相关的一般图中边的分类

摘要

我们研究了一个 Hermitian 矩阵的特征值的重数的变化，该矩阵的图是一个一般的无向图，当从图中移除一条边时。在先前的工作中已经研究了当图是树时的相同问题。在这里，我们根据相邻顶点的状态给出一般图中边的可能分类。事实证明，有四种情况确实发生在一般图中但不能发生在树中。