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On computing total double Roman domination number of trees in linear time
2020Let $G=(V,E)$ be a graph. A doubleRoman dominating function (DRDF) on $G$ is a function$f:Vto{0,1,2,3}$ such that for every vertex $vin V$if $f(v)=0$, then either there is a vertex $u$ adjacent to $v$ with $f(u)=3$ orthere are vertices $x$ and $y$ adjacent to $v$ with $f(x)=f(y)=2$ and if $f(v)=1$, then there is a vertex $u$ adjacent to $v$ with$f(u ...
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An Upper Bound on the Total Roman { 2 } -domination Number of Graphs with Minimum Degree Two
Journal of Combinatorial Mathematics and Combinatorial ComputingA total Roman \(\{2\}\)-dominating function on a graph \(G = (V,E)\) is a function \(f:V\rightarrow\{0,1,2\}\) with the properties that (i) for every vertex \({v}\in V\) with \(f({v})=0\), \(f(N({v}))\ge2\) and (ii) the set of vertices with \(f({v})>0\) induces a subgraph with no isolated vertices.
Kheibari, M. +3 more
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Signed total Roman domination and domatic numbers in graphs
Applied Mathematics and ComputationYubao Guo, Lutz Volkmann, Yun Wang 0042
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Roman {3}-domination (double Italian domination)
Discrete Applied Mathematics, 2020Doost Ali Mojdeh, Lutz Volkmann
exaly
Varieties of Roman domination II
AKCE International Journal of Graphs and Combinatorics, 2020Mustapha Chellali +2 more
exaly
Triple Roman domination in graphs
Applied Mathematics and Computation, 2021H Abdollahzadeh Ahangar
exaly
Constructive characterizations concerning weak Roman domination in trees
Discrete Applied Mathematics, 2020Ismael G Yero, Abel Cabrera Martinez
exaly