Results 11 to 20 of about 419,100 (266)
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.
Kalinowski, Thomas +2 more
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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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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 ...
Gentner, Michael, Rautenbach, Dieter
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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.
Gentner, Michael +3 more
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Forcing Parameters in Fully Connected Cubic Networks
Mathematics, 2022 Domination in graphs has been extensively studied and adopted in many real life applications. The monitoring electrical power system is a variant of a domination problem called power domination problem.
Yongsheng Rao +4 more
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An Inverse Approach for Finding Graphs with a Failed Zero Forcing Number of k
Mathematics, 2023 For a 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 included in S.
Chirag Kaudan +2 more
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On the Zero Forcing Number and Spectral Radius of Graphs [PDF]
The Electronic Journal of Combinatorics, 2022 In this paper, we determine the graphs (respectively, trees) with maximum spectral radius among all graphs (respectively, trees) with zero forcing number at most $k$. As an application, we give a sharp lower bound for the zero forcing number of graphs involving the spectral radius.
Zhang, Wenqian +3 more
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Characterization of All Graphs with a Failed Skew Zero Forcing Number of 1
Mathematics, 2022 Given a graph G, the zero forcing number of G, Z(G), is the minimum cardinality of any set S of vertices of which repeated applications of the forcing rule results in all vertices being in S.
Aidan Johnson +2 more
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Open global shadow graph and it’s zero forcing number
Proyecciones (Antofagasta), 2023 Zero forcing number of a graph is the minimum cardinality of the zero forcing set. A zero forcing set is a set of black vertices of minimum cardinality that can colour the entire graph black using the color change rule: each vertex of G is coloured either white or black, and vertex v is a black vertex and can force a white neighbour only if it has one ...
Raksha, M. R., Dominic, Charles
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Throughput, Spectral, and Energy Efficiency of 5G Massive MIMO Applications Using Different Linear Precoding Schemes [PDF]
International Journal of Electronics and Telecommunications, 2023 On fifth-generation wireless networks, a potential massive MIMO system is used to meet the ever-increasing request for high-traffic data rates, high-resolution streaming media, and cognitive communication.
Ibrahim Salah +3 more
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