The acyclic matrices with a P-set of maximum size

被引：11
作者：
Du, Zhibin [1 ]
da Fonseca, Carlos M. [2 ]
机构：
[1] Zhaoqing Univ, Sch Math & Informat Sci, Zhaoqing 526061, Peoples R China
[2] Kuwait Univ, Dept Math, Safat 13060, Kuwait
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 468卷
关键词：
Trees; Acyclic matrices; Multiplicity of eigenvalues; P-set; P-vertices; NUMBER; MULTIPLICITIES; VERTICES;
D O I：
10.1016/j.laa.2013.10.042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let m(A) (0) denote the nullity of a given matrix A of order n. Set A(alpha) for the principal submatrix of A obtained after deleting the rows and columns indexed by the nonempty subset a of {1, . . . , n}. When m(A(alpha))(0) = m(A)(0) + |alpha|, we call alpha a P-set of A. In this paper, we classify all of the trees T for which there exists a matrix A whose graph is T and containing a P-set of maximum size. Our characterization does not depend on whether the acyclic matrices are singular or nonsingular. (C) 2013 Elsevier Inc. All rights reserved.
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收藏
页码：27 / 37
页数：11
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