Results 41 to 50 of about 26,712 (151)
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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The Zero (Total) Forcing Number and Covering Number of Trees
Taiwanese Journal of MathematicsSummary: Let \(F(G)\), \(F_t (G)\), \(\beta (G)\), and \(\beta^\prime(G)\) be the zero forcing number, the total forcing number, the vertex covering number and the edge covering number of a graph \(G\), respectively. In this paper, we first completely characterize all trees \(T\) with \(F(T) = (\Delta -2) \beta (T)+1\), solving a problem proposed by ...
Tu, Dongxin, Li, Jianxi, Shiu, Wai-Chee
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On the zero forcing number of some Cayley graphs [PDF]
Algebraic structures and their applications, 2017 Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices ...
Vatandoost, Ebrahim +1 more
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Zero forcing number of graphs with a power law degree distribution [PDF]
Physical Review E, 2021 The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbour colour forcing rule. The zero forcing number provides topological information about linear algebra on graphs, with applications to the controllability of linear dynamical systems and quantum walks on graphs among other problems.
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IEEE Access, 2016 This paper investigates a multi-pair two-way massive MIMO amplify-and-forward full-duplex relay (FDR) system over Ricean fading channels, where multiple pairs of full-duplex users exchange information within pair through a full-duplex relay with a very ...
Xiaoli Sun +5 more
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Failed Skew Zero Forcing Numbers of Path Powers and Circulant Graphs
AppliedMathFor a graph G, the zero forcing number of G, Z(G), is defined to be the minimum cardinality of a set S of vertices for which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is as follows: if a vertex v is in
Aidan Johnson +3 more
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A Worst Case Performance Analysis of Approximated Zero Forcing Vectoring for DSL Systems
Information, 2018 In this paper we introduce a Gaussian approximation for the achievable downstream bit rate per user in modern broadband and ultra-broadband digital subscriber loop-based access systems.
Franco Mazzenga, Romeo Giuliano
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A computational comparison of compact MILP formulations for the zero forcing number [PDF]
Discrete Applied Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agostinho Agra +2 more
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Zero forcing number, Grundy domination number, and their variants [PDF]
Linear Algebra and its Applications, 2019 This paper presents strong connections between four variants of the zero forcing number and four variants of the Grundy domination number. These connections bridge the domination problem and the minimum rank problem. We show that the Grundy domination type parameters are bounded above by the minimum rank type parameters.
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Zero Forcing Number of Some Families of Graphs
Mohyla Mathematical Journal, 2021 The work is devoted to the study of the zero forcing number of some families of graphs. The concept of zero forcing is a relatively new research topic in discrete mathematics, which already has some practical applications, in particular, is used in studies of the minimum rank of the matrices of adjacent graphs. The zero forcing process is an example of
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