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Disprove of a conjecture on the double Roman domination number
Aequationes mathematicaeThe paper addresses a conjecture regarding the double Roman domination number \(\gamma_{dR}(G)\) in graph theory, a topic introduced by \textit{R. A. Beeler} et al. [Discrete Appl. Math. 211, 23--29 (2016; Zbl 1348.05146)]. The double Roman dominating function (DRDF) \(f: V \to \{0, 1, 2, 3\}\) on a graph \(G = (V, E)\) requires specific conditions on ...
Z. Shao +4 more
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On the Outer Independent Total Double Roman Domination in Graphs [PDF]
Mediterranean Journal of Mathematics, 2023 A double Roman dominating function (DRDF) on a graph $$G=(V,E)$$ G = ( V , E ) is a function $$f:V\rightarrow \{0,1,2,3\}$$ f : V → { 0 , 1 , 2 , 3 } satisfying (i) if $$f(v)=0$$ f ( v ) = 0 , then there must be at least two neighbors assigned 2 under f ...
H. Ahangar +3 more
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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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Independent double roman domination number of a tree in terms of its 2-independence number
Discrete Mathematics, Algorithms and ApplicationsLet [Formula: see text] be a simple graph. An independent double Roman dominating function (IDRDF) on a graph [Formula: see text] is a function [Formula: see text] having the property that first if [Formula: see text], then vertex [Formula: see text] has at least two neighbors assigned [Formula: see text] under [Formula: see text] or one neighbor ...
Halimeh Koulivand +3 more
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Outer independent double Roman domination
Applied Mathematics and Computation, 2020An outer independent double Roman dominating function (OIDRDF) of a graph G is a function h from V(G) to {0, 1, 2, 3} for which each vertex with label 0 is adjacent to a vertex with label 3 or at least two vertices with label 2, and each vertex with ...
Mustapha Chellali, S M Sheikholeslami
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Notes on double Roman domination edge critical graphs
RAIRO Oper. Res.Given a graph G=(V,E), a double Roman dominating function (DRDF) on a graph G is a function f:V→{0,1,2,3} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=3 or two vertices v₁ and v₂ for ...
A. Omar, A. Bouchou
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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 ...
A. Poureidi
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Research on the Double Roman Domination Number of Some Special Graphs
Advances in Applied Mathematics, 2022沙沙 刘
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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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Signed double Roman domination numbers in digraphs
Annals of the University of Craiova - Mathematics and Computer Science Series, 2021"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2, 3\}$ satisfying the following conditions: (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the ...
Jafar Amjadi, Fatemeh Pourhosseini
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