Positive semidefinite zero forcing

被引：28

作者：

Ekstrand, Jason ^{[1
]}

Erickson, Craig ^{[1
]}

Hall, H. Tracy ^{[2
]}

Hay, Diana ^{[1
]}

Hogben, Leslie ^{[1
,3
]}

Johnson, Ryan ^{[1
]}

Kingsley, Nicole ^{[1
]}

Osborne, Steven ^{[1
]}

Peters, Travis ^{[1
]}

Roat, Jolie ^{[1
]}

Ross, Arianne ^{[1
]}

Row, Darren D. ^{[4
]}

Warnberg, Nathan ^{[1
]}

Young, Michael ^{[1
]}

机构：

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[2] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[3] Amer Inst Math, Palo Alto, CA 94306 USA

[4] Upper Iowa Univ, Sch Sci & Math, Fayette, IA 52142 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 439卷 / 07期

基金：

美国国家科学基金会;

关键词：

Zero forcing number; Maximum nullity; Minimum rank; Positive semidefinite; Matrix; Graph; MINIMUM-RANK; MATRICES; NULLITY; GRAPHS;

D O I：

10.1016/j.laa.2013.05.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The positive semidefinite zero forcing number Z(+)(G) of a graph G was introduced in Barioli et al. (2010) [4]. We establish a variety of properties of Z(+)(G): Any vertex of G can be in a minimum positive semidefinite zero forcing set (this is not true for standard zero forcing). The graph parameters tw(G) (tree-width), Z(+)(G), and Z(G) (standard zero forcing number) all satisfy the Graph Complement Conjecture (see Barioli et al. (2012) [3]). Graphs having extreme values of the positive semidefinite zero forcing number are characterized. The effect of various graph operations on positive semidefinite zero forcing number and connections with other graph parameters are studied. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1862 / 1874

页数：13

共 21 条

[1]

[Anonymous], 2006, AM I MATH WORKSH SPE

[2] Zero forcing sets and the minimum rank of graphs [J].

Barioli, Francesco ;

Barrett, Wayne ;

Butler, Steve ;

Cioaba, Sebastian M. ;

Cvetkovic, Dragos ;

Fallat, Shaun M. ;

Godsil, Chris ;

Haemers, Willem ;

Hogben, Leslie ;

Mikkelson, Rana ;

Narayan, Sivaram ;

Pryporova, Olga ;

Sciriha, Irene ;

So, Wasin ;

Stevanovic, Dragan ;

van der Holst, Hein ;

Vander Meulen, Kevin N. ;

Wehe, Amy Wangsness .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (07) :1628-1648

[3]

Barioli F, 2011, ELECTRON J LINEAR AL, V22, P10

[4] On the graph complement conjecture for minimum rank [J].

Barioli, Francesco ;

Barrett, Wayne ;

Fallat, Shaun M. ;

Hall, H. Tracy ;

Hogben, Leslie ;

van der Holst, Hein .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (12) :4373-4391

[5] Zero forcing parameters and minimum rank problems [J].

Barioli, Francesco ;

Barrett, Wayne ;

Fallat, Shaun M. ;

Hall, H. Tracy ;

Hogben, Leslie ;

Shader, Bryan ;

van den Driessche, P. ;

van der Holst, Hein .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (02) :401-411

[6]

Barrett W, 2004, ELECTRON J LINEAR AL, V11, P258

[7]

Barrett W, 2009, ELECTRON J LINEAR AL, V18, P530

[8] ON THE MINIMUM RANK AMONG POSITIVE SEMIDEFINITE MATRICES WITH A GIVEN GRAPH [J].

Booth, Matthew ;

Hackney, Philip ;

Harris, Benjamin ;

Johnson, Charles R. ;

Lay, Margaret ;

Mitchell, Lon H. ;

Narayan, Sivaram K. ;

Pascoe, Amanda ;

Steinmetz, Kelly ;

Sutton, Brian D. ;

Wang, Wendy .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (02) :731-740

[9]

Borie R.B., 2004, HDB GRAPH THEORY, P99

[10]

BRUALDI R, 2007, AIM WORKSH SPECTR FA

← 1 2 3 →