Results 211 to 220 of about 405 (227)

DOUBLE ROMAN DOMINATION NUMBER OF MIDDLE GRAPH

South East Asian J. of Mathematics and Mathematical Sciences, 2022
For any graph G(V,  E), a function f : V (G)    0, 1, 2, 3     is called Double Roman dominating function (DRDF) if the following properties holds, If f (v) = 0, then there exist two vertices v1, v2 ∈ N (v) for which f (v1) = f (v2) = 2 or there exist one vertex u ∈ N (v) for which f (u) = 3.∈ If f (v) = 1, then there exist one vertex u N (v) for which
Shirkol, Shailaja S., Kumbargoudra, Pavitra P., Kaliwal, Meenal M.   +2 more
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Weak Double Roman Domination

Bulletin of the Malaysian Mathematical Sciences Society
The authors introduce a new variant of domination in graphs called weak double Roman domination (WDRD), which generalizes the well-studied concept of double Roman domination (DRD) by relaxing certain constraints. Given a graph \( G = (V, E) \), a WDRD-function is a labeling \( f: V \to \{0,1,2,3\} \) that satisfies the following condition: every vertex
Soltani, S., Ahangar, H. Abdollahzadeh, Chellali, M., Rahbani, H., Sheikholeslami, S. M.   +4 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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Critical concept for double Roman domination in graphs

Discrete Mathematics, Algorithms and Applications, 2020
A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices assigned a [Formula: see text] or to at least one vertex assigned a [Formula: see text] and (ii) every vertex [Formula: see text] with ...
Sakineh Nazari-Moghaddam, Lutz Volkmann
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Double Roman Domination in Cartesian Product

Creative Mathematics and Informatics
Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\in N(v)$ such that $f(v_{1})=2=f(v_{2})$ or there exists $ w \in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then there exists $ w \in N(v)$ such that $f(w)\geq 2$ is called a double Roman dominating function (DRDF). The
Anu, V., Aparna, Lakshmanan S.
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An Upper Bound on the Double Roman Domination Number

Bulletin of the Iranian Mathematical Society, 2020
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Ouldrabah, Lyes, Volkmann, Lutz
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Double Roman domination in some graphs

Discrete Mathematics, Algorithms and Applications
A double Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions that if [Formula: see text], then every vertex v is adjacent to minimum one vertex u for which [Formula: see text] or two vertices [Formula: see text] and [Formula: see text] for which [Formula: see text] and if [Formula: see ...
J. Meena, T. N. M. Malini Mai, M. L. Suresh, Laxmi Rathour, Lakshmi Narayan Mishra   +4 more
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On the complexity of perfect Roman domination and perfect double Roman domination

Discrete Mathematics, Algorithms and Applications
For a graph [Formula: see text] and a function [Formula: see text], let [Formula: see text] ([Formula: see text]) be the set of vertices assigned the value [Formula: see text] by [Formula: see text]. A perfect Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula ...
Seyed Hosein Mirhoseini, Nader Jafari Rad, Noor A’lawiah Abd Aziz, Hailiza Kamarulhaili   +3 more
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Algorithmic results on double Roman domination in graphs

Journal of Combinatorial Optimization, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sumanta Banerjee, Michael A. Henning, Dinabandhu Pradhan   +2 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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