Positive Semidefinite Zero Forcing

Date
2013-10-01
Authors
Ekstrand, Jason
Erickson, Craig
Hall, H. Tracy
Hogben, Leslie
Hay, Diana
Hogben, Leslie
Johnson, Ryan
Kingsley, Nicole
Osborne, Steven
Peters, Travis
Roat, Jolie
Ross, Arianne
Row, Darren
Warnberg, Nathan
Young, Michael
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Mathematics
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Abstract

The positive semidefinite zero forcing number Z+(G) of a graph G was introduced in [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 [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.

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<p>This is a manuscript of an article published as Ekstrand, Jason, Craig Erickson, H. Tracy Hall, Diana Hay, Leslie Hogben, Ryan Johnson, Nicole Kingsley et al. "Positive semidefinite zero forcing."<em> Linear Algebra and its Applications</em> 439, no. 7 (2013): 1862-1874. DOI: <a href="http://dx.doi.org/10.1016/j.laa.2013.05.020" target="_blank">10.1016/j.laa.2013.05.020</a>. Posted with permission.</p>
Keywords
Zero forcing number, Maximum nullity, Minimum rank, Positive semidefinite, Matrix, Graph
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