Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree

Johnson CR; Jordan-Squire C; Sher DA

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Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree

机译：特征值分配和Hermitian矩阵（图中的树）中的两个最大多重性

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Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree we focus upon M-2, the maximum value of the sum of the two largest multiplicities. The corresponding M-1 is already understood. The notion of assignment (of eigenvalues to subtrees) is formalized and applied. Using these ideas, simple upper and lower bounds are given for M-2 (in terms of simple graph theoretic parameters), cases of equality are indicated, and a combinatorial algorithm is given to compute M-2 precisely. In the process, several techniques are developed that likely have more general uses.

机译：在图为一棵树的Hermitian矩阵特征值的可能多重性列表中，我们关注M-2，这是两个最大多重性之和的最大值。相应的M-1已经被理解。（特征值到子树的）分配概念被形式化和应用。利用这些思想，给出了M-2的简单上限和下限（根据简单的图形理论参数），指出了等价情况，并给出了组合算法来精确地计算M-2。在此过程中，开发了几种可能具有更普遍用途的技术。

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《Discrete Applied Mathematics》 |2010年第6期|共11页
作者
Johnson CR; Jordan-Squire C; Sher DA;
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正文语种 eng
中图分类离散数学;
关键词
Eigenvalue multiplicities; Symmetric matrices; Trees; Two largest multiplicities;

机译：特征值多重性;对称矩阵;树;两个最大多重性;

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专利

1. Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree [J] . Johnson CR, Jordan-Squire C, Sher DA Discrete Applied Mathematics . 2010,第6期

机译：特征值分配和Hermitian矩阵（图中的树）中的两个最大多重性
2. On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree [J] . Da Fonseca CM Annali di matematica pura ed applicata . 2008,第2期

机译：图为树的厄米矩阵的特征值的多重性
3. On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree [J] . C. M. Da Fonseca Annali di Matematica Pura ed Applicata . 2008,第2期

机译：图为树的埃尔米特矩阵特征值的多重性
4. On the Largest Eigenvalue of Signless Laplacian Matrix of Halin Graphs [C] . Xiaoxin Zhu, Yajuan Wu International conference on application of mathematics and physics;AMP2010 . 2010

机译：Halin图的无符号拉普拉斯矩阵的最大特征值
5. Partial Eigenvalue Assignment Problem for the Quadratic Matrix Pencil. [D] . Tarannum, Husna. 2009

机译：二次矩阵铅笔的部分特征值分配问题。
6. Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs [O] . Yong Lu, Ligong Wang, Qiannan Zhou -1

机译：混合图的Hermitian-Randić矩阵和Hermitian-Randić能量
7. Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree [O] . Johnson Charles R., Jordan-Squire Christopher, Sher David A. 2010

机译：特征图赋值和Hermitian矩阵（图是树）中的两个最大多重性
8. The Eigenvalues of a Partitioned Hermitian Matrix Involving a Parameter. [R] . Thompson, R. C. 1973

机译：含参数的分割Hermitian矩阵的特征值。

Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree

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