Positive semidefinite zero forcing

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Abstract

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. © 2013 Elsevier Inc. All rights reserved.

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Ekstrand, J., Erickson, C., Hall, H. T., Hay, D., Hogben, L., Johnson, R., … Young, M. (2013). Positive semidefinite zero forcing. Linear Algebra and Its Applications, 439(7), 1862–1874. https://doi.org/10.1016/j.laa.2013.05.020

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