Positive semidefinite zero forcing

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 t...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 439; no. 7; pp. 1862 - 1874
Main Authors Ekstrand, Jason, Erickson, Craig, Hall, H. Tracy, Hay, Diana, Hogben, Leslie, Johnson, Ryan, Kingsley, Nicole, Osborne, Steven, Peters, Travis, Roat, Jolie, Ross, Arianne, Row, Darren D., Warnberg, Nathan, Young, Michael
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2013
Subjects
Graph
Matrix
Maximum nullity
Minimum rank
Positive semidefinite
Zero forcing number
Zero forcing number
Positive semidefinite
Minimum rank
Matrix
Graph
Maximum nullity
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2013.05.020