The effect of removing a 2-downer edge or a cut 2-downer edge triangle for an eigenvalue

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2023-01-01 DOI:10.1515/spma-2022-0186

K. Toyonaga

引用次数: 0

Abstract

Abstract Edges in the graph associated with a square matrix over a field may be classified as to how their removal affects the multiplicity of an identified eigenvalue. There are five possibilities: + 2 +2 (2-Parter); + 1 +1 (Parter); no change (neutral); − 1 -1 (downer); and − 2 -2 (2-downer). Especially, it is known that 2-downer edges for an eigenvalue comprise cycles in the graph. We investigate the effect for the statuses of other edges or vertices by removing a 2-downer edge. Then, we investigate the change in the multiplicity of an eigenvalue by removing a cut 2-downer edge triangle.

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为特征值移除2-下行边或切割2-下行边三角形的效果

在一个域上与方阵相关的图中的边可以根据它们的移除如何影响已识别特征值的多重性来分类。有五种可能:+2 +2 (2- partner);+1 +1(合作伙伴);No change(中性);−1 -1(下行);−2 -2 (2-down)。特别是，已知一个特征值的2下边包含图中的环。我们通过移除一条2向下的边来研究对其他边或顶点状态的影响。然后，我们研究了通过去除切割2-下边三角形特征值的多重性的变化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.