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Further Progress on the Total Roman $$\{2\}$$-Domination Number of Graphs

Bulletin of the Iranian Mathematical Society, 2021
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Abdollahzadeh Ahangar, Hossein, Chellali, Mustapha, Hajjari, Maryam, Sheikholeslami, Seyed Mahmoud   +3 more
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Total double Roman domination numbers in digraphs

Discrete Mathematics, Algorithms and Applications, 2021
Let [Formula: see text] be a finite and simple digraph with vertex set [Formula: see text]. A double Roman dominating function (DRDF) on digraph [Formula: see text] is a function [Formula: see text] such that every vertex with label 0 has an in-neighbor with label 3 or two in-neighbors with label 2 and every vertex with label 1 have at least one in ...
Amjadi, J., Pourhosseini, F.
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New bounds on the outer-independent total double Roman domination number

Discrete Mathematics, Algorithms and Applications, 2023
A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying (i) if [Formula: see text] then there must be at least two neighbors assigned two under [Formula: see text] or one neighbor [Formula: see text] with [Formula: see text]; and (ii) if [Formula: see text] then [Formula: see text] must be ...
S. M. Sheikholeslami, L. Volkmann
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Twin signed total Roman domination numbers in digraphs

Asian-European Journal of Mathematics, 2018
Let [Formula: see text] be a finite simple digraph with vertex set [Formula: see text] and arc set [Formula: see text]. A twin signed total Roman dominating function (TSTRDF) on the digraph [Formula: see text] is a function [Formula: see text] satisfying the conditions that (i) [Formula: see text] and [Formula: see text] for each [Formula: see text ...
Amjadi, J., Soroudi, M.
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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 Computing
A 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., Ahangar, H. Abdollahzadeh, Khoeilar, R., Sheikholeslami, S. M.   +3 more
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On computing total double Roman domination number of trees in linear time

2020
Let $G=(V,E)$ 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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Total Roman {2}-domination in graphs

Quaestiones Mathematicae, 2021
Abel Cabrera Martínez, Frank Angel Hernandez Mira, Ismael G Yero   +2 more
exaly  

Signed total Roman domination and domatic numbers in graphs

Applied Mathematics and Computation
Yubao Guo, Lutz Volkmann, Yun Wang
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Total Roman {3}-domination in Graphs

Symmetry, 2020
Zehui Shao, Doost Ali Mojdeh
exaly  

Total Roman domination in the lexicographic product of graphs

Discrete Applied Mathematics, 2019
Dorota Kuziak
exaly