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Majority double Roman domination in graphs
Discrete Mathematics, Algorithms and Applications, 2023A majority double Roman dominating function (MDRDF) 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 with 2 or to at least one vertex [Formula: see text] with [Formula: see text], (ii) every vertex [Formula: see text ...
Anandha Prabhavathy, S., Sahul Hamid, I.
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Inverse double Roman domination in graphs
Discrete Mathematics, Algorithms and Applications, 2022For a graph [Formula: see text], a double Roman dominating function (DRDF) is a function [Formula: see text] such that each vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices labeled [Formula: see text] or one vertex labeled [Formula: see text] and each vertex [Formula: see text] with [Formula: see text] is ...
D' Souza, Wilma Laveena +2 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, 2021Sierpiński 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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Outer independent signed double Roman domination
Journal of Applied Mathematics and Computing, 2021Suppose $$[3]=\{0,1,2,3\}$$ and $$[3^{-}]=\{-1,1,2,3\}$$ . An outer independent signed double Roman dominating function (OISDRDF) of a graph
Ahangar, H. Abdollahzadeh +3 more
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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. +4 more
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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. +4 more
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Total double Roman domination numbers in digraphs
Discrete Mathematics, Algorithms and Applications, 2021Let [Formula: see text] be a finite and simple digraph with vertex set [Formula: see text]. A double Roman dominating function (DRDF) on digraph [Formula: see text] is a function [Formula: see text] such that every vertex with label 0 has an in-neighbor with label 3 or two in-neighbors with label 2 and every vertex with label 1 have at least one in ...
Amjadi, J., Pourhosseini, F.
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Double Roman Domination in Cartesian Product
Creative Mathematics and InformaticsGiven 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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Global double Roman domination in graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2019A double Roman dominating function (DRDF) on a graph G = (V, E) is a function f : V(G) → {0, 1, 2, 3} having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2...
Zehui Shao +3 more
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Signed double Roman domination numbers in digraphs
Annals of the University of Craiova - Mathematics and Computer Science Series, 2021"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2, 3\}$ satisfying the following conditions: (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the ...
Jafar Amjadi, Fatemeh Pourhosseini
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On the Global Double Roman Domination of Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guoliang Hao, Xiaodan Chen
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