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Bounds on the global double Roman domination number in graphs
Discussiones Mathematicae Graph Theory, 2022 Summary: Let \(G\) be a simple graph of order \(n\) and let \(\gamma_{\mathrm{gdR}}(G)\) be the global double Roman domination number of \(G\). In this paper, we give some upper bounds on the global double Roman domination number of \(G\). In particular, we completely characterize the graph \(G\) with \(\gamma_{\mathrm{gdR}}(G)=2n-2\) and \(\gamma_ ...
Guoliang Hao +3 more
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Double Roman domination number
Discrete Applied Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aparna Lakshmanan S
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The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) [PDF]
Mathematics, 2018 A double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to { 0 , 1 , 2 , 3 } in such a way that a vertex u for which f ( u ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f ( u ) = 1 has at least a neighbor labeled 2 or 3.
Huiqin Jiang, Pu Wu, Zehui Shao
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More results on the signed double Roman domination number of graphs
AKCE International Journal of Graphs and CombinatoricsPublished by Dep.
Sheikholeslami, Seyed Mahmoud +1 more
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Bounds on the total double Roman domination number of graphs
Discussiones Mathematicae Graph Theory, 2023 Summary: Let \(G\) be a simple graph with no isolated vertex and let \(\gamma_{tdR}(G)\) be the total double Roman domination number of \(G\). In this paper, we present lower and upper bounds on \(\gamma_{tdR}(G)\) of a graph \(G\) in terms of the order, open packing number and the numbers of support vertices and leaves, and we characterize all ...
Guoliang Hao +3 more
semanticscholar +3 more sources
Double Roman domination and domatic numbers of graphs [PDF]
Communications in Combinatorics and Optimization, 2018 Summary: A double Roman dominating function on a graph \(G\) with vertex set \(V(G)\) is defined in [\textit{R. A. Beeler} et al., Discrete Appl. Math. 211, 23--29 (2016; Zbl 1348.05146)] as a function \(f:V(G)\rightarrow\{0,1,2,3\}\) having the property that if \(f(v)=0\), then the vertex \(v\) must have at least two neighbors assigned 2 under \(f ...
L. Volkmann
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An improved upper bound on the independent double Roman domination number of trees
AKCE International Journal of Graphs and Combinatorics, 2022 AbstractFor a graph [Formula: see text] an independent double Roman dominating function (IDRDF) is a function [Formula: see text] having the property that: (i) every vertex [Formula: see text] with f(v) = 0 has a neighbor u with f(u) = 3 or at least two neighbors x and y such that [Formula: see text] (ii) every vertex [Formula: see text] with f(v) = 1 ...
F. Nahani Pour +3 more
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Some Progress on the Double Roman Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V ā {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
N. J. Rad, Hadi Rahbani
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On the Outer Independent Double Roman Domination Number [PDF]
Bulletin of the Iranian Mathematical Society, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Doost Ali Mojdeh +3 more
semanticscholar +5 more sources
Discrete Applied Mathematics, 2016 For a graph G=(V,E), a double Roman dominating function is a function f:Vā{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 with f(w)=3, and if f(v)=1, then vertex v must have ...
TERESA W Haynes, Stephen T Hedetniemi
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