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Critical ideals, minimum rank and zero forcing number [PDF]
Applied Mathematics and Computation, 2019 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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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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Reconfiguration graphs of zero forcing sets
Discrete Applied Mathematics, 2023Jesse Geneson +2 more
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On the zero forcing number of graphs and their splitting graphs
2019Summary: In [10], the notion of the splitting graph of a graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph \(\Gamma\) of order \(n \geqslant 2\), \(Z[S(\Gamma)]\leqslant 2 Z(\Gamma)\) and
Chacko, B. +2 more
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Computational approaches for zero forcing and related problems
European Journal of Operational Research, 2019Boris Brimkov, Illya V Hicks
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On the Zero Forcing Number of Complementary Prism Graphs
2023DOMINIC, CHARLES, RAKSHA, M R
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