Fundamental graphs for the maximum multiplicity of an eigenvalue among Hermitian matrices with a given graph

IF 0.8 Q2 MATHEMATICS
Charles R. Johnson, António Leal-Duarte, Carlos M. Saiago
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引用次数: 0

Abstract

Our purpose is to identify the graphs that are “fundamental” for the maximum multiplicity problem for Hermitian matrices with a given undirected simple graph. Like paths for trees, these are the special graphs to which the maximum multiplicity problem may be reduced. These are the graphs for which maximum multiplicity implies that all vertices are downers. Examples include cycles and complete graphs, and several more are identified, using the theory developed herein. All the unicyclic graphs that are fundamental, are explicitly identified. We also list those graphs with two edges added to a tree, and their maximum multiplicities, which we have found so far to be fundamental. A formula for maximum multiplicity is given based on fundamental graphs.

具有给定图的厄米矩阵中特征值的最大多重性的基本图
我们的目的是识别具有给定无向简单图的厄米矩阵的最大多重性问题的“基本”图。就像树的路径一样,这些是可以简化最大多重性问题的特殊图。这些图的最大多重性意味着所有顶点都是向下的。例子包括循环和完全图,以及使用本文开发的理论确定的其他几个。所有基本的单环图,都被明确地标识出来。我们还列出了那些有两条边加到树上的图,以及它们的最大复数,这是我们迄今为止发现的最基本的。在基本图的基础上,给出了最大多重性的计算公式。
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
55
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