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Double Roman Domination: A Survey
Mathematics, 2023 Since 2016, when the first paper of the double Roman domination appeared, the topic has received considerable attention in the literature. We survey known results on double Roman domination and some variations of the double Roman domination, and a list ...
Darja Rupnik Poklukar, Janez Žerovnik
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On the Total Double Roman Domination [PDF]
IEEE Access, 2019 Let G = (V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u) = 0, then u must have at least two neighbors assigned 2 or one neighbor assigned 3 under f ...
Zehui Shao +3 more
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Complexity of Roman {2}-domination and the double Roman domination in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 For a simple, undirected graph a Roman {2}-dominating function (R2DF) has the property that for every vertex with f(v) = 0, either there exists a vertex with f(u) = 2, or at least two vertices with The weight of an R2DF is the sum The minimum weight of ...
Chakradhar Padamutham +1 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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Discharging Approach for Double Roman Domination in Graphs
IEEE Access, 2018 The discharging method is most well-known for its central role in the proof of the Four Color Theorem. This proof technique was extensively applied to study various graph coloring problems, in particular on planar graphs.
Zehui Shao +5 more
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Quasi total double Roman domination in graphs
AKCE International Journal of Graphs and CombinatoricsA quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
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Double Roman and double Italian domination
Discussiones Mathematicae Graph Theory, 2023 Summary: Let \(G\) be a graph with vertex set \(V(G)\). A double Roman dominating function (DRDF) on a graph \(G\) is a function \(f:V(G)\longrightarrow\{0,1,2,3\}\) that satisfies the following conditions: (i) If \(f(v)=0\), then \(v\) must have a neighbor \(w\) with \(f(w)=3\) or two neighbors \(x\) and \(y\) with \(f(x)=f(y)=2\); (ii) If \(f(v)=1\),
Lutz Volkmann
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Some Properties of Double Roman Domination [PDF]
Discrete Dynamics in Nature and Society, 2020 A double Roman dominating function on a graph G is a function f:VG⟶0,1,2,3 satisfying the conditions that every vertex u for which fu=0 is adjacent to at least one vertex v for which fv=3 or two vertices v1 and v2 for which fv1=fv2=2 and every vertex u ...
Hong Yang, Xiaoqing Zhou
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Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
TERESA Haynes, Stephen T Hedetniemi
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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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