Throttling positive semidefinite zero forcing propagation time on graphs
نویسندگان
چکیده
منابع مشابه
Zero forcing propagation time on oriented graphs
Zero forcing is an iterative coloring procedure on a graph that starts by initially coloring vertices white and blue and then repeatedly applies the following rule: if any blue vertex has a unique (out-)neighbor that is colored white, then that neighbor is forced to change color from white to blue. An initial set of blue vertices that can force the entire graph to blue is called a zero forcing ...
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Zero forcing is a game played on a graph that starts with a coloring of the vertices as white and black and at each step any vertex colored black with a unique neighbor colored white “forces” the color of the white vertex to become black. In this note we look at what happens when we balance the size of the initial set of vertices colored black and the number of steps, called speed of propagaion...
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Abstract. Let G be a simple, undirected graph. Positive semidefinite (PSD) zero forcing on G is based on the following 1 color-change rule: Let W1,W2, . . . ,Wk be the sets of vertices of the k connected components in G − B (where B is a set of blue 2 vertices). If w ∈Wi is the only white neighbor of some b ∈ B in the graph G[B∪Wi], then we change w to blue. A minimum positive 3 semidefinite ze...
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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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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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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.06.017