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The Zero Forcing Number of Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2019 A subset S of initially infected vertices of a graph G is called zero forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbor, infects this neighbor.
Thomas Kalinowski +2 more
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All Graphs with a Failed Zero Forcing Number of Two [PDF]
Symmetry, 2021 Given a graph G, the zero forcing number of G, Z(G), is the smallest cardinality of any set S of vertices on which repeated applications of the forcing rule results in all vertices being in S.
Karla Rubi +3 more
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On graphs maximizing the zero forcing number
Discrete Applied Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shou-Jun Xu
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Some bounds on the zero forcing number of a graph
Discrete Applied Mathematics, 2018 A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if initially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$, and then, iteratively and as long as possible, changing the label of some vertex $u$ from $0$ to $1$ if $u$ is the only neighbor with label $0$ of some vertex with label $1$, results in the ...
Dieter Rautenbach, Michael Gentner
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On Extremal Graphs for Zero Forcing Number
Graphs and Combinatorics, 2022For a graph \(G\) with \(S\subseteq V(G)\), \(S\) is a zero forcing set of \(G\) if iteratively adding vertices to \(S\) from \(V(G)\setminus S\) that are the unique neighbor in \(V(G)\setminus S\) of some vertex in \(S\), results in the entire \(V(G)\) of \(G\).
Yi-Ping Liang, Jianxi Li, Shou-Jun Xu
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Positive semidefinite zero forcing [PDF]
Linear Algebra and Its Applications, 2013 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).
Craig Erickson +2 more
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Extremal values and bounds for the zero forcing number
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Uéverton S Souza +2 more
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Proof of a conjecture on the zero forcing number of a graph
Discrete Applied Mathematics, 2016 8 ...
Baoyindureng Wu
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The Zero Forcing Number of Graphs with the Matching Number and the Cyclomatic Number
Graphs and Combinatorics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu Jing, Wenqian Zhang, Shengjin Ji
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Fractional zero forcing via three-color forcing games [PDF]
Discrete Applied Mathematics, 2016 An r-fold analogue of the positive semidefinite zero forcing process that is carried out on the r-blowup of a graph is introduced and used to define the fractional positive semidefinite forcing number.
David Robérson +2 more
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