Results 261 to 270 of about 9,485,710 (280)

On the Zero Forcing Number of Trees

Iranian Journal of Science and Technology, Transactions A: Science, 2021
Let 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 in iterated line digraphs

Discrete Applied Mathematics, 2019
Zero forcing is a propagation process on a graph, or digraph, defined in linear algebra to provide a bound for the minimum rank problem. Independently, zero forcing was introduced in physics, computer science and network science, areas where line ...
Sudeep Stephen, Thomas Kalinowski, Daniela Ferrero   +2 more
exaly   +2 more sources

Zero forcing number of fuzzy graphs with application

Journal of Intelligent & Fuzzy Systems, 2020
We 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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Zero forcing and maximum nullity for hypergraphs [PDF]

Discrete Applied Mathematics, 2020
The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is described by a ...
Leslie Hogben
exaly   +1 more source

On Zero Forcing Number of Permutation Graphs

2012
Zero 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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Some results on the total (zero) forcing number of a graph

Journal of Combinatorial Optimization
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Jianxi Li, Dongxin Tu, Wai Chee Shiu
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The zero forcing number of claw-free cubic graphs

Discrete Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mengya He, Huixian Li, Ning Song, Shengjin Ji   +3 more
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The Zero Forcing Number of Quartic Circulant Graphs of Prime Order

Ars Combinatoria
Let \( G \) be a graph, the zero forcing number \( Z(G) \) is the minimum of \( |Z| \) over all zero forcing sets \( Z \subseteq V(G) \). In this paper, we are interested in studying the zero forcing number of quartic circulant graphs \( C_{p}\left(s,t\right) \), where \( p \) is an odd prime. Based on the fact that \( C_{p}\left(s,t\right) \cong C_{p}\
Huixian Li, Guang Li, Shengjin Ji
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Reconfiguration graphs of zero forcing sets

Discrete Applied Mathematics, 2023
Leslie Hogben, Ruth Haas, Jesse Geneson   +2 more
exaly  

On the zero forcing number of graphs and their splitting graphs

2019
Summary: 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., Dominic, C., Premodkumar, K.P.   +2 more
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