Results 11 to 20 of about 1,017,243 (285)
Zero forcing irredundant sets [PDF]
Australas. J Comb.Irredundance has been studied in the context of dominating sets, via the concept of private neighbor. Here irredundance of zero forcing sets is introduced via the concept of a private fort and the upper and lower zero forcing irrdedundance numbers $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are defined.
Bryan Curtis +2 more
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Zero forcing in Benzenoid network
Proyecciones (Antofagasta), 2019 A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)\S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring.
Anitha, J., Rajasingh, Indra
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We introduce randomized zero forcing (RZF), a stochastic color-change process on directed graphs in which a white vertex turns blue with probability equal to the fraction of its incoming neighbors that are blue. Unlike probabilistic zero forcing, RZF is governed by in-neighborhood structure and can fail to propagate globally due to directionality.
Jesse Geneson +4 more
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An approximation algorithm for zero forcing
Discrete Applied MathematicsWe give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\text{pw}(G)+1$, where $\text{pw}(G)$ is the pathwidth of $G$. Starting from a path decomposition, the algorithm runs in $O(nm)$ time, where $n$ and $m$ are the order and size of the graph, respectively.
Ben Cameron +3 more
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Rigid Linkages and Partial Zero Forcing [PDF]
The Electronic Journal of Combinatorics, 2019 Connections between vital linkages and zero forcing are established. Specifically, the notion of a rigid linkage is introduced as a special kind of unique linkage and it is shown that spanning forcing paths of a zero forcing process form a spanning rigid linkage and thus a vital linkage.
Daniela Ferrero +7 more
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Variations of zero forcing and power domination [PDF]
, 2021 Zero forcing is a propagation process on a graph that turns white vertices into blue vertices. In this process, an initial set of vertices in a graph $G$ are chosen to be blue and all others are colored white, then a color-change rule is iteratively applied until all of $G$ becomes blue.
Alameda, Joseph
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Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph [PDF]
Neutrosophic Sets and Systems, 2022 New setting is introduced to study dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophicnumber, independent number, independent neutrosophic ...
Henry Garrett
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GRAPHS WITH TOTAL FORCING NUMBER TWO, REVISITED [PDF]
Journal of Algebraic Systems, 2021 A subset of the vertex set of a graph $G$ is called a zero forcing set if by considering them colored and, as far as possible, a colored vertex with exactly one non-colored neighbor forces its non-colored neighbor to get colored, then the whole vertices ...
M. Alishahi, E. Rezaei-Sani
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Connected zero forcing sets and connected propagation time of graphs [PDF]
Transactions on Combinatorics, 2020 The zero forcing number $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ with colored (black) vertices which forces the set $V(G)$ to be colored (black) after some times.
Maryam Khosravi +2 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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