THE NUMBER OF P-VERTICES OF SINGULAR ACYCLIC MATRICES: AN INVERSE PROBLEM

被引：1

作者：

Du, Zhibin ^{[1
,2
]}

da Fonseca, Carlos M. ^{[3
,4
]}

机构：

[1] South China Normal Univ, Sch Software, Foshan 528225, Guangdong, Peoples R China

[2] Zhaoqing Univ, Sch Math & Stat, Zhaoqing 526061, Peoples R China

[3] Kuwait Coll Sci & Technol, Block 4,POB 27235, Safat 13133, Kuwait

[4] Univ Primorska, FAMNIT, Glagoljsaska 8, Koper 6000, Slovenia

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2020年 / 40卷 / 02期

基金：

中国国家自然科学基金;

关键词：

trees; acyclic matrices; singular; multiplicity of eigenvalues; P-set; P-vertices; SET; ORDER;

D O I：

10.7151/dmgt.2282

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a real symmetric matrix. If after we delete a row and a column of the same index, the nullity increases by one, we call that index a P-vertex of A. When A is an n x n singular acyclic matrix, it is known that the maximum number of P-vertices is n - 2. If T is the underlying tree of A, we will show that for any integer number k is an element of {0, 1,..., n - 2}, there is a (singular) matrix whose graph is T and with k P-vertices. We will provide illustrative examples.

引用

页码：525 / 532

页数：8

共 16 条

[1]

Ager M, 2010, 2010 INFORMATION THEORY AND APPLICATIONS WORKSHOP (ITA), P75

[2] Nonsingular acyclic matrices with full number of P-vertices [J].

Andelic, Milica ;

Eric, Aleksandra ;

da Fonseca, C. M. .

LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (01) :49-57

[3] On the number of P-vertices of some graphs [J].

Andelic, Milica ;

da Fonseca, C. M. ;

Mamede, Ricardo .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (02) :514-525

[4]

Du Z., 2016, J. South China Normal Univ. Natur. Sci. Ed., V48, P119

[5] The number of P-vertices for acyclic matrices of maximum nullity [J].

Du, Zhibin ;

da Fonseca, Carlos M. .

DISCRETE APPLIED MATHEMATICS, 2019, 269 :211-219

[6] On the continuity of the maximum size of P-sets of acyclic matrices [J].

Du, Zhibin ;

da Fonseca, Carlos M. .

DISCRETE MATHEMATICS, 2019, 342 (08) :2278-2282

[7] The Singular Acyclic Matrices of Even Order with a P-Set of Maximum Size [J].

Du, Zhibin ;

da Fonseca, Carlos M. .

FILOMAT, 2016, 30 (13) :3403-3409

[8] The real symmetric matrices of odd order with a P-set of maximum size [J].

Du, Zhibin ;

da Fonseca, Carlos M. .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2016, 66 (03) :1007-1026

[9] The acyclic matrices with a P-set of maximum size [J].

Du, Zhibin ;

da Fonseca, Carlos M. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 468 :27-37

[10] Nonsingular acyclic matrices with an extremal number of P-vertices [J].

Du, Zhibin ;

da Fonseca, C. M. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 442 :2-19

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