Results 131 to 140 of about 10,626,776 (155)

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 ...
Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +1 more
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An upper bound on the double Roman domination number

Journal of Combinatorial Optimization, 2018
From the summary: ``A double Roman dominating function (DRDF) on a graph \(G=(V, E)\) is a function \(f: V\to \{0,1, 2, 3\}\) having the property that if \(f(v)=0\), then vertex \(v\) must have at least two neighbors assigned \(2\) under \(f\) or one neighbor \(w\) with \(f(w)=3\), and if \(f(v)=1\), then vertex \(v\) must have at least one neighbor ...
Jafar Amjadi, Sakineh Nazari-Moghaddam, Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +3 more
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On the double Roman domination number in trees

Australas. J Comb., 2020
Summary: For a graph \(G\), let \(\gamma_{dR}(G)\) and \(\gamma_R(G)\) denote the double Roman domination number and the Roman domination number, respectively. In this paper, we show that for every tree \(T\) of order \(n\geq 3\), with \(\ell(T)\) leaves and \(s(T)\) support vertices, \begin{align*} \gamma_R(T)+\lceil & \frac{\ell(T)-s(T)}{\Delta(T ...
Sakineh Nazari-Moghaddam, Mustapha Chellali   +1 more
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Extremal Digraphs for an Upper Bound on the Double Roman Domination Number

Bulletin of the Malaysian Mathematical Sciences Society, 2019
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Ouldrabah, Lyes, Blidia, Mostafa, Bouchou, Ahmed, Volkmann, Lutz   +3 more
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A note on the double Roman domination number of graphs

Czechoslovak Mathematical Journal, 2019
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Disprove of a conjecture on the double Roman domination number

Aequationes mathematicae
The 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, R. Khoeilar, H. Karami, M. Chellali, S. M. Sheikholeslami   +4 more
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An improved upper bound on the double Roman domination number of graphs with minimum degree at least two

Discrete Applied Mathematics, 2019
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Rana Khoeilar, Hossein Karami 0002, Mustapha Chellali, Seyed Mahmoud Sheikholeslami   +3 more
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Bounds on the quasi-total double Roman domination number in graphs

Discrete Mathematics, Algorithms and Applications
A 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, S. Babaei, S. M. Sheikholeslami, M. Chellali, S. Kosari   +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 Applications
Let [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, Mohammad Habibi, Hassan Arianpoor, Mina Valinavaz   +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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