The number of P-vertices in a matrix with maximum nullity

被引:4
|
作者
Fernandes, Rosario [1 ,2 ]
da Cruz, Henrique F. [3 ]
机构
[1] Univ Nova Lisboa, CMA, P-2829516 Caparica, Portugal
[2] Univ Nova Lisboa, Fac Ciencias & Tecnol, P-2829516 Caparica, Portugal
[3] Univ Beira Interior, Ctr Matemat & Aplicacoes CMA UBI, Rua Marques DAvila & Bolama, P-6201001 Covilha, Portugal
关键词
Trees; Acyclic matrices; Maximum nullity; Parter vertices; EIGENVALUE; MULTIPLICITY; GRAPH; TREE; SETS;
D O I
10.1016/j.laa.2018.02.018
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let T be a tree with n >= 2 vertices. Set 8(T) for the set of all real symmetric matrices whose graph is T. Let A is an element of S(T) and i is an element of {1, . . . , n}. We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set m(A) (0) for the multiplicity of the eigenvalue zero in A (the nullity of A). When m(A(i)) (0) = m(A) (0) + 1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B is an element of S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A is an element of S(T) with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E is an element of S(T) with b P-vertices and maximum nullity. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码:168 / 182
页数:15
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