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The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a 2-linear tree
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2022-03-19 , DOI: 10.1080/03081087.2022.2049186 Wenxuan Ding 1 , Matthew Ingwersen 2 , Charles R. Johnson 1
中文翻译:
图为二元线性树的实对称矩阵中重数为1的特征值的最小个数
更新日期:2022-03-19
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2022-03-19 , DOI: 10.1080/03081087.2022.2049186 Wenxuan Ding 1 , Matthew Ingwersen 2 , Charles R. Johnson 1
Affiliation
For a tree T, denotes the minimum number of eigenvalues of multiplicity 1 among all real symmetric matrices, whose graph is T. It is known that . A tree is linear if all its vertices of degree at least 3 lie on a single induced path, and k-linear if there are k of these high degree vertices. is known for generalized stars (1-linear trees), and is determined here for 2-linear trees. Three (and higher) linear trees offer considerable additional complications.
中文翻译:
图为二元线性树的实对称矩阵中重数为1的特征值的最小个数
对于树T,表示所有实对称矩阵中重数为 1 的特征值的最小个数,其图形为T。众所周知. 如果一棵树的所有度数至少为 3 的顶点都位于一条诱导路径上,则该树是线性的,如果存在k 个这些高度数的顶点,则为k线性树。以广义恒星(1-线性树)而闻名,并且此处为 2 线性树确定。三棵(或更多)线性树提供了相当多的额外复杂性。