On the complexity of the positive semidefinite zero forcing number
نویسندگان
چکیده
منابع مشابه
On the Complexity of the Positive Semidefinite Zero Forcing Number
The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and the fast-mixed searching, which implies some NP-completeness results for the zero forcing problem. For chordal graphs much is understood regarding the relat...
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Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the col...
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The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...
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The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...
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The maximum positive semidefinite nullity of a multigraph G is the largest possible nullity over all real positive semidefinite matrices whose (i, j)th entry (for i 6= j) is zero if i and j are not adjacent in G, is nonzero if {i, j} is a single edge, and is any real number if {i, j} is a multiple edge. The definition of the positive semidefinite zero forcing number for simple graphs is extende...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.03.011