The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph
The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph
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埃尔米特矩阵特征值重数的变化与从图中删除边相关
DOI：
10.1016/j.disc.2010.10.010
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Paul R. McMichael
中科院分区：
文献类型：
--
作者：
Charles R. Johnson;Paul R. McMichael
当从无向图中移除边时，该图的埃尔米特矩阵的特征值的重数可能会发生有限的变化。主要针对树木，我们识别可能发生的变化并描述它们发生的环境。这扩展了移除顶点的已知结果。给出了一系列示例来说明可能发生的可能性，并将树的情况与一般图的情况进行对比。
When an edge is removed from an undirected graph, there is a limited change that can occur in the multiplicity of an eigenvalue of a Hermitian matrix with that graph. Primarily for trees, we identify the changes that can occur and characterize the circumstances under which they occur. This extends known results for the removal of vertices. A catalog of examples is given to illustrate the possibilities that can occur and to contrast the case of trees with that of general graphs.