图描述的空矩阵的特征值反及相关问题

IF 0.7 4区 数学 Q2 Mathematics Electronic Journal of Linear Algebra Pub Date : 2022-02-05 DOI:10.13001/ela.2022.6941
F. S. Dahlgren, Zachary Gershkoff, L. Hogben, S. Motlaghian, Derek Young
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引用次数: 1

摘要

由图$G$描述的空心矩阵是一个实对称矩阵,其所有对角条目都等于零,并且非对角条目由$G$中的邻接控制。对于给定的图$G$,与$G$相关的矩阵的所有可能谱的确定是$G$的空心逆特征值问题。给出了路径和完全二部图的空心特征值反问题的解。对于附加的图族,给出了相关子问题的结果,如可能的有序多重性列表、特征值的最大多重性和不同特征值的最小数量。
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Inverse eigenvalue and related problems for hollow matrices described by graphs
A hollow matrix described by a graph $G$ is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in $G$. For a given graph $G$, the determination of all possible spectra of matrices associated with $G$ is the hollow inverse eigenvalue problem for $G$. Solutions to the hollow inverse eigenvalue problems for paths and complete bipartite graphs are presented. Results for related subproblems such as possible ordered multiplicity lists, maximum multiplicity of an eigenvalue, and minimum number of distinct eigenvalues are presented for additional families of graphs.
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
期刊最新文献
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