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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. The zero forcing number of G is the minimum cardinality of a zero forcing set in G.
Thomas Kalinowski +2 more
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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 ...
Michael Gentner, Dieter Rautenbach
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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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On graphs maximizing the zero forcing number
Discrete Applied Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yi-Ping Liang, Shou-Jun Xu
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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.
Michael Gentner +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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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. The forcing rule is: if a vertex v is in S, and exactly one neighbor u of v is not in S, then u is added to S in the next iteration.
Luis Gomez +3 more
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On the Zero Forcing Number of Trees
Iranian Journal of Science and Technology, Transactions A: Science, 2021Let G be a graph such that the color of its vertices is white or black. A dynamic vertex coloring for G is defined as follows. One starts with a certain set of black vertices. Then, at each time step, a black vertex with exactly one white neighbor forces its white neighbor to become black.
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Zero forcing number of fuzzy graphs with application
Journal of Intelligent & Fuzzy Systems, 2020We introduce and study forcing number for fuzzy graphs. Also, we compute zero forcing numbers for some classes of graphs and extend this concept to fuzzy graphs. In this regard we obtain upper bounds for zero forcing of some classes of fuzzy graphs. We will proceed to obtain a new algorithm to computing zero forcing set and finding a formula for zero ...
Asefeh Karbasioun, Reza Ameri
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