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Roman domination and independent Roman domination on graphs with maximum degree three
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Luiz
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On the double Roman domination of graphs
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Yue
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On the Roman domination polynomials
2023Summary: A Roman dominating function (RDF) on a graph \(G\) is a function \(f:V(G)\to \{0,1,2\}\) satisfying the condition that every vertex \(u\) with \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\). The weight of an RDF \(f\) is the sum of the weights of the vertices under \(f\). The Roman domination number, \(\gamma_R(G)\
Jafari Rad, Nader +1 more
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Graphs and Combinatorics, 2015
For a simple graph \(G=(V,E)\), a Roman dominating function \(f:V\rightarrow \{0,1,2\}\) has the property that every vertex \(v\in V\) with \(f(v)=0\) has a neighbor \(u\) with \(f(u)=2\). The Roman domination number of \(G\) is the minimum weight of a Roman dominating function on \(G\), which is defined as \(f(V)=\sum_{v\in V} f(v)\).
Chellali, Mustapha +4 more
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For a simple graph \(G=(V,E)\), a Roman dominating function \(f:V\rightarrow \{0,1,2\}\) has the property that every vertex \(v\in V\) with \(f(v)=0\) has a neighbor \(u\) with \(f(u)=2\). The Roman domination number of \(G\) is the minimum weight of a Roman dominating function on \(G\), which is defined as \(f(V)=\sum_{v\in V} f(v)\).
Chellali, Mustapha +4 more
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Quaestiones Mathematicae, 2015
A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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Relations between the Roman k-domination and Roman domination numbers in graphs
Discrete Mathematics, Algorithms and Applications, 2014Let G = (V, E) be a graph and let k be a positive integer. A Roman k-dominating function ( R k-DF) on G is a function f : V(G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices v1, v2, …, vk with f(vi) = 2 for i = 1, 2, …, k.
Ahmed Bouchou +2 more
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Global Roman Domination in Trees
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maryam Atapour +2 more
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Resolving Roman domination in graphs
Discrete Mathematics, Algorithms and Applications, 2021Let [Formula: see text] be a graph and [Formula: see text] be a Roman dominating function defined on [Formula: see text]. Let [Formula: see text] be some ordering of the vertices of [Formula: see text]. For any [Formula: see text], [Formula: see text] is defined by [Formula: see text].
P. Roushini Leely Pushpam +2 more
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Comput. Biol. Medicine
The Spiking Neural Network (SNN) is a third-generation neural network recognized for its energy efficiency and ability to process spatiotemporal information, closely imitating the behavioral mechanisms of biological neurons in the brain. SNN exhibit rich
Raja Sekhar Banovoth, Kadambari K V
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The Spiking Neural Network (SNN) is a third-generation neural network recognized for its energy efficiency and ability to process spatiotemporal information, closely imitating the behavioral mechanisms of biological neurons in the brain. SNN exhibit rich
Raja Sekhar Banovoth, Kadambari K V
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Extremal Bounds of the Atom-Bond Connectivity Index in Trees with a Fixed Roman Domination Number
Malaysian journal of mathematical sciencesLet G = (X, Y) be a simple, connected graph, where X denotes the set of vertices and Y represents the set of edges. The atom-bond connectivity (ABC) index, introduced by Estrada et al. [10], is a topological descriptor used in mathematical chemistry.
W. Ali, M. Husin, M. F. Nadeem
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