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Proof of a Conjecture on the Zero Forcing Number of a Graph
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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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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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Critical Ideals, Minimum Rank and Zero Forcing Number [PDF]
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical ideal is trivial. This gives a new perspective for bounding and computing these three graph parameters.
Carlos A Alfaro, Jephian C.-H. Lin
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On the Zero Forcing Number of Bijection Graphs
2016The zero forcing number of a graph is a graph parameter based on a color change process, which starts with a state, where all vertices are colored either black or white. In the next step a white vertex turns black, if it is the only white neighbor of some black vertex, and this step is then iterated.
Denys Shcherbak +2 more
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Fractional Zero Forcing via Three-Color Forcing Games [PDF]
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 E Robérson +2 more
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On Zero Forcing Number of Permutation Graphs
2012Zero forcing number, Z(G), of a graph G is the minimum cardinality of a set S of black vertices (whereas vertices in \(V(G)\!\setminus\!S\) are colored white) such that V(G) is turned black after finitely many applications of “the color-change rule”: a white vertex is converted black if it is the only white neighbor of a black vertex.
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The zero forcing number of claw-free cubic graphs
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mengya He +3 more
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Some results on the total (zero) forcing number of a graph
Journal of Combinatorial OptimizationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianxi Li, Dongxin Tu, Wai Chee Shiu
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