Positive semidefinite zero forcing

被引：26

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 50 条

[41] Fuzzification of Zero Forcing Process
Borzooei, R. A.
Hoseini, B. Sheikh
Golmohammadian, M.
Montazeri, Z.
Takallo, M. Mohseni
NEW MATHEMATICS AND NATURAL COMPUTATION, 2020, 16 (01) : 195 - 210
[42] The zero forcing polynomial of a graph
Boyer, Kirk
Brimkov, Boris
English, Sean
Ferrero, Daniela
Keller, Ariel
Kirsch, Rachel
Phillips, Michael
Reinhart, Carolyn
DISCRETE APPLIED MATHEMATICS, 2019, 258 : 35 - 48
[43] A NOTE ON VARIANTS OF ZERO FORCING
Mitchell, Lon
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2019, 35 : 468 - 472
[44] Zero forcing for sign patterns
Goldberg, Felix
Berman, Abraham
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 447 : 56 - 67
[45] On the complexity of failed zero forcing
Shitov, Yaroslav
THEORETICAL COMPUTER SCIENCE, 2017, 660 : 102 - 104
[46] The Zero Forcing Span of a Graph
Jacob, Bonnie
COMBINATORICS, GRAPH THEORY AND COMPUTING, SEICCGTC 2021, 2024, 448 : 255 - 267
[47] On the Zero Forcing Number of Trees
Oboudi, Mohammad Reza
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2021, 45 (03): : 1065 - 1070
[48] Throttling for zero forcing and variants
Carlson, Joshua
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2019, 75 : 96 - 112
[49] Zero forcing with random sets
Curtis, Bryan
Gan, Luyining
Haddock, Jamie
Lawrence, Rachel
Spiro, Sam
DISCRETE MATHEMATICS, 2024, 347 (05)
[50] THE ZERO FORCING NUMBER OF GRAPHS
Kalinowski, Thomas
Kamcev, Nina
Sudakov, Benny
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2019, 33 (01) : 95 - 115

← 1 2 3 4 5 →