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Bounds on the global double Roman domination number in graphs [PDF]

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, Shouliu Wei, Seyed Mahmoud Sheikholeslami, Xiaodan Chen   +3 more
doaj   +3 more sources

An improved upper bound on the independent double Roman domination number of trees [PDF]

AKCE International Journal of Graphs and Combinatorics, 2022
For 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 ...
F. Nahani Pour, H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami   +3 more
doaj   +3 more sources

Double Roman domination and domatic numbers of graphs [PDF]

Communications in Combinatorics and Optimization, 2018
A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} 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 ...
L. Volkmann
doaj   +4 more sources

More results on the signed double Roman domination number of graphs

AKCE International Journal of Graphs and Combinatorics
A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a ...
Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +1 more
doaj   +4 more sources

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, Babak Samadi, Zehui Shao, Ismael G. Yero   +3 more
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The double Roman domination number of generalized Sierpiński graphs [PDF]

Discrete Mathematics, Algorithms and Applications, 2020
In this paper, we study the double Roman domination number of generalized Sierpiński graphs [Formula: see text]. More precisely, we obtain a bound for the double Roman domination number of [Formula: see text]. We also find the exact value of [Formula: see text].
Anu, V., Lakshmanan, S. Aparna
  +6 more sources

Bounds on the total double Roman domination number of graphs [PDF]

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 ...
Hao, Guoliang, Xie, Zhihong, Sheikholeslami, Seyed Mahmoud, Hajjari, Maryam   +3 more
openaire   +2 more sources

On the double Roman domination number in oriented trees [PDF]

, 2023
Abstract Note: Please see pdf for full abstract with equations. Let D = (V,A) be a digraph. A double Roman dominating function on a digraph D is a function ƒ :V → {0, 1, 2, 3} such that every vertex u for which ƒ(u) = 0 has an in-neighbor v for which ƒ(v) = 3 or at least two in-neighbors assigned 2 under ƒ, while if ƒ(u) = 1, then the vertex u ...
Lyes Ouldrabah, Ahmed Bouchou, Mostafa Blidia   +2 more
openaire   +2 more sources

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
openaire   +4 more sources

Impact of Some Graph Operations on Double Roman Domination Number [PDF]

, 2019
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 $f(v_{1})=f(v_{2})=2$ 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).
V., Anu, S., Aparna Lakshmanan
openaire   +3 more sources