Results 11 to 20 of about 107,030 (250)
On Two Outer Independent Roman Domination Related Parameters in Torus Graphs
Mathematics, 2022 In a graph G=(V,E), where every vertex is assigned 0, 1 or 2, f is an assignment such that every vertex assigned 0 has at least one neighbor assigned 2 and all vertices labeled by 0 are independent, then f is called an outer independent Roman dominating ...
Hong Gao +3 more
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A note on the independent roman domination in unicyclic graphs [PDF]
Opuscula Mathematica, 2012 A Roman dominating function (RDF) on a graph \(G = (V;E)\) is a function \(f : V \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\).
Mustapha Chellali, Nader Jafari Rad
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Further results on outer independent triple Roman domination
AKCE International Journal of Graphs and CombinatoricsAn outer-independent triple Roman dominating function (OI[3]RDF) on a graph [Formula: see text] is function [Formula: see text] having the property that (i) if [Formula: see text] then v must have either a neighbor assigned 4 or two neighbors one of ...
F. Najafi +4 more
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Independent double Roman domination in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 For a graph G = (V,E), a double Roman dominating function has the property that for every vertex with f(v) = 0, either there exists a vertex , with f(u) = 3, or at least two neighbors having f(x) = f(y) = 2, and every vertex with value 1 under f has at ...
H. R. Maimani +3 more
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Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
Discussiones Mathematicae Graph Theory, 2013 A Roman dominating function (RDF) on a graph G = (V,E) is 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 v for which f(v) = 2.
Chellali Mustapha, Rad Nader Jafari
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Discussiones Mathematicae Graph Theory, 2022 A 2-rainbow dominating function (2RDF) of a graph G is a function g from the vertex set V (G) to the family of all subsets of {1, 2} such that for each vertex v with g(v) =∅ we have ∪u∈N(v) g(u) = {1, 2}.
Poureidi Abolfazl, Rad Nader Jafari
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On the Outer-Independent Roman Domination in Graphs [PDF]
Symmetry, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. Let Vi={v∈V(G):f(v)=i} for every i∈{0,1,2}. The function f is an outer-independent Roman dominating function on G if V0 is an independent set and every vertex in V0 is adjacent to at least one vertex in V2.
Abel Cabrera Martínez +3 more
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Independent Roman Domination Stable and Vertex-Critical Graphs
IEEE Access, 2018 A Roman dominating function (RDF) on a graph $G$ is a function $f: V(G) \rightarrow \{0, 1, 2\}$ for which every vertex assigned 0 is adjacent to a vertex assigned 2. The weight of an RDF is the value $\omega (f) = \sum _{u \in V(G)}f(u)$ .
Pu Wu +5 more
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On the Outer-Independent Double Roman Domination of Graphs [PDF]
Frontiers in Applied Mathematics and Statistics, 2021 An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex ...
Yongsheng Rao +4 more
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Independent [k]-Roman domination on graphs
Discussiones Mathematicae Graph TheoryGiven a function $f\colon V(G) \to \mathbb{Z}_{\geq 0}$ on a graph $G$, $AN(v)$ denotes the set of neighbors of $v \in V(G)$ that have positive labels under $f$. In 2021, Ahangar et al.~introduced the notion of $[k]$-Roman Dominating Function ([$k$]-RDF) of a graph $G$, which is a function $f\colon V(G) \to \{0,1,\ldots,k+1\}$ such that $\sum_{u \in N ...
Atílio Luiz, Francisco Anderson Vieira
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