Results 281 to 290 of about 128,027 (302)
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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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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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Roman domination in signed graphs
2022Summary: Let \(S = (G, \sigma)\) be a signed graph. A function \(f: V \rightarrow \{0,1,2\}\) is a Roman dominating function on \(S\) if (i) for each \(v \in V\), \(f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma (uv) f(u) \geq 1\) and (ii) for each vertex \(v\) with \(f(v) = 0\) there exists a vertex \(u\in N^+(v)\) such that \(f(u) = 2\).
Joseph, James, JOSEPH, MAYAMMA
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Mixed Roman Domination in Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ahangar, H. Abdollahzadeh +2 more
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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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Roman Domination Dot-critical Graphs
Graphs and Combinatorics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jafari Rad, Nader, Volkmann, Lutz
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Global Roman Domination in Trees
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Atapour, M. +2 more
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Double Roman Domination in Digraphs
Bulletin of the Malaysian Mathematical Sciences Society, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guoliang Hao +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
Kumar, M. Kamal, Reddy, L. Sudershan
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Bulletin of the Malaysian Mathematical Sciences Society
The authors introduce a new variant of domination in graphs called weak double Roman domination (WDRD), which generalizes the well-studied concept of double Roman domination (DRD) by relaxing certain constraints. Given a graph \( G = (V, E) \), a WDRD-function is a labeling \( f: V \to \{0,1,2,3\} \) that satisfies the following condition: every vertex
Soltani, S. +4 more
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The authors introduce a new variant of domination in graphs called weak double Roman domination (WDRD), which generalizes the well-studied concept of double Roman domination (DRD) by relaxing certain constraints. Given a graph \( G = (V, E) \), a WDRD-function is a labeling \( f: V \to \{0,1,2,3\} \) that satisfies the following condition: every vertex
Soltani, S. +4 more
openaire +1 more source