Results 221 to 230 of about 426 (246)

Double Roman domination subdivision number in graphs

Asian-European Journal of Mathematics, 2021
For a graph [Formula: see text], a double Roman dominating function is a function [Formula: see text] having the property that if [Formula: see text], then vertex [Formula: see text] must have at least two neighbors assigned [Formula: see text] under [Formula: see text] or one neighbor with [Formula: see text], and if [Formula: see text], then vertex [
Amjadi, J., Sadeghi, H.
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Twin signed double Roman domination numbers in directed graphs

Discrete Mathematics, Algorithms and Applications, 2022
Let [Formula: see text] be a finite simple directed graph (shortly digraph). A function [Formula: see text] is called a twin signed double Roman dominating function (TSDRDF) if (i) every vertex [Formula: see text] with [Formula: see text] has at least two in-neighbor assigned a 2 or at least an in-neighbor [Formula: see text] with [Formula: see text],
Akram Mahmoodi, Maryam Atapour, Sattar Aliyar   +2 more
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On the double Roman domination number in trees [PDF]

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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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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Roman Domination and Double Roman Domination Numbers of Sierpiński Graphs $$S(K_n,t)$$

Bulletin of the Malaysian Mathematical Sciences Society, 2021
Sierpiński graph \(S_n^t\) can be defined recursively as \(S_n^1\cong K_n\) and one obtains \(S_n^{t+1}\) from \(S_n^t\) by replacing each vertex from \(S_n^t\) by a copy of \(K_n\) and adding some special edges between these copies of \(K_n\). Let \(G\) be a graph.
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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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