Results 11 to 20 of about 1,075,663 (288)
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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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, Joseph Alameda
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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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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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Propagation time for probabilistic zero forcing [PDF]
CoRR, 2018 Zero forcing is a coloring game played on a graph that was introduced more than ten years ago in several different applications. The goal is to color all the vertices blue by repeated use of a (deterministic) color change rule. Probabilistic zero forcing was introduced by Kang and Yi in [Probabilistic zero forcing in graphs, Bull. Inst. Combin.
Geneson, Jesse, Hogben, Leslie
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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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Probabilistic zero forcing on random graphs [PDF]
European Journal of Combinatorics, 2021 Zero forcing is a deterministic iterative graph coloring process in which vertices are colored either blue or white, and in every round, any blue vertices that have a single white neighbor force these white vertices to become blue. Here we study probabilistic zero forcing, where blue vertices have a non-zero probability of forcing each white neighbor ...
Sean English +2 more
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Properties of a q-Analogue of Zero Forcing [PDF]
Graphs and Combinatorics, 2020 Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one single vertex at the cost of a single token; or if any currently filled vertex has a unique non-filled neighbor ...
Steve Butler +8 more
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RIS-Aided Zero-Forcing and Regularized Zero-Forcing Beamforming in Integrated Information and Energy Delivery [PDF]
IEEE Transactions on Wireless Communications, 2022 This paper considers a network of a multi-antenna array base station (BS) and a reconfigurable intelligent surface (RIS) to deliver both information to information users (IUs) and power to energy users (EUs). The RIS links the connection between the IUs and the BS as there is no direct path between the former and the latter.
Hongwen Yu +4 more
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