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Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teresa W Haynes, Stephen T Hedetniemi
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Triple Roman domination in graphs
Applied Mathematics and Computation, 2021 The Roman domination in graphs is well-studied in graph theory. The topic is related to a defensive strategy problem in which the Roman legions are settled in some secure cities of the Roman Empire. The deployment of the legions around the Empire is designed in such a way that a sudden attack to any undefended city could be quelled by a legion from a ...
Mustapha Chellali, S M Sheikholeslami
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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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On the double Roman domination in graphs
Discrete Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hossein Abdollahzadeh Ahangar +2 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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INVERSE ROMAN DOMINATION IN GRAPHS
Discrete Mathematics, Algorithms and Applications, 2013Motivated by the article in Scientific American [7], Michael A Henning and Stephen T Hedetniemi explored the strategy of defending the Roman Empire. Cockayne defined Roman dominating function (RDF) on a Graph G = (V, E) to be a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex
M. Kamal Kumar, L. Sudershan Reddy
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