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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
Shailaja S. Shirkol +2 more
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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
Vaibhav Anu, LAKSHMANAN S. APARNA
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A note on the double Roman domination number of graphs [PDF]
Discrete Applied Mathematics, 2020 summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor with $f(w)
Chen, Xue-Gang
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On the Independent Double Roman Domination in Graphs [PDF]
Bulletin of the Iranian Mathematical Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Doost Ali Mojdeh, Zhila Mansouri
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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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Bounds on the global double Roman domination number in graphs [PDF]
Discussiones Mathematicae Graph Theory, 2022 Guoliang Hao +3 more
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Outer independent double Roman domination number of graphs [PDF]
Bulletin of the Iranian Mathematical Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Doost Ali Mojdeh +3 more
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More results on the signed double Roman domination number of graphs
AKCE International Journal of Graphs and CombinatoricsA 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 +1 more
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Outer Independent Double Roman Domination Stability in Graphs [PDF]
Ars CombinatoriaAn outer independent double Roman dominating function (OIDRDF) on a graph G is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that (i) if f ( v ) = 0 , then the 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 the vertex v must have at least one ...
Seyed Mahmoud Sheikholeslami +2 more
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Signed double Roman domination on cubic graphs
Applied Mathematics and ComputationThe signed double Roman domination problem is a combinatorial optimization problem on a graph asking to assign a label from $\{\pm{}1,2,3\}$ to each vertex feasibly, such that the total sum of assigned labels is minimized. Here feasibility is given whenever (i) vertices labeled $\pm{}1$ have at least one neighbor with label in $\{2,3\}$; (ii) each ...
Enrico Iurlano +3 more
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