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Total double Roman domination numbers in digraphs
Discrete Mathematics, Algorithms and Applications, 2021Let [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 ...
Jafar Amjadi, F. Pourhosseini
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Further Progress on the Total Roman $$\{2\}$$-Domination Number of Graphs
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdollahzadeh Ahangar, Hossein +3 more
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New bounds on the outer-independent total double Roman domination number
Discrete Mathematics, Algorithms and Applications, 2023A 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 ...
Seyed Mahmoud Sheikholeslami +1 more
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Bounds on weak roman and 2-rainbow domination numbers [PDF]
Discrete Applied Mathematics, 2014 We mainly study two related dominating functions, namely, the weak Roman and 2-rainbow dominating functions. We show that for all graphs, the weak Roman domination number is bounded above by the 2-rainbow domination number.
TERESA Haynes, Stephen T Hedetniemi
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Bounds on the quasi-total double Roman domination number in graphs
Discrete Mathematics, Algorithms and ApplicationsA 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 [Formula: see text], then vertex [Formula: see text] must have at least two neighbors assigned 2 under [Formula: see text] or one neighbor [Formula: see text] with [Formula: see text]; (ii) if [
J. Amjadi +4 more
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On the outer-independent total (Roman) domination number of some graph operators
RAIRO - Operations ResearchThe goal of this article is to obtain closed formulas for the outer-independent total domination number and the outer-independent total Roman domination number of the following well-known graph operators defined from a connected graph $G$: the central graph $\mathtt{C}(G)$, the middle graph $\mathtt{M}(G)$, the graph operator $\mathtt{R}(G)$ and the ...
Ismael Rios-Villamar +2 more
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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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