Results 21 to 30 of about 2,319,231 (271)
Bounds on the Double Italian Domination Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2022 For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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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
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Double Roman Domination in Generalized Petersen Graphs P(ck, k)
Symmetry, 2022 A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3}, satisfying the condition that every vertex u for which f(u)=1 is adjacent to at least one vertex assigned 2 or 3, and every vertex u with f(u)=0 is adjacent to at least ...
D. R. Poklukar, J. Žerovnik
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Perfect double Italian domination of a graph
AKCE International Journal of Graphs and Combinatorics, 2023 For a graph [Formula: see text] with [Formula: see text] and [Formula: see text], a perfect double Italian dominating function is a function [Formula: see text] having the property that [Formula: see text], for every vertex [Formula: see text] with ...
Guoliang Hao +2 more
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On the Outer Independent Total Double Roman Domination in Graphs [PDF]
Mediterranean Journal of Mathematics, 2023 A double Roman dominating function (DRDF) on a graph $$G=(V,E)$$ G = ( V , E ) is a function $$f:V\rightarrow \{0,1,2,3\}$$ f : V → { 0 , 1 , 2 , 3 } satisfying (i) if $$f(v)=0$$ f ( v ) = 0 , then there must be at least two neighbors assigned 2 under f ...
H. A. Ahangar +3 more
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On the Double Roman Domination in Generalized Petersen Graphs P(5k,k)
Mathematics, 2022 A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and every vertex u with f(u)
Darja Rupnik Poklukar, Janez Žerovnik
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Notes on double Roman domination edge critical graphs
RAIRO Oper. Res.Given a graph G=(V,E), a double Roman dominating function (DRDF) on a graph G is a function f:V→{0,1,2,3} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=3 or two vertices v₁ and v₂ for ...
A. Omar, A. Bouchou
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On Two Outer Independent Roman Domination Related Parameters in Torus Graphs
Mathematics, 2022 In a graph G=(V,E), where every vertex is assigned 0, 1 or 2, f is an assignment such that every vertex assigned 0 has at least one neighbor assigned 2 and all vertices labeled by 0 are independent, then f is called an outer independent Roman dominating ...
Hong Gao +3 more
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Bounds on the Hop Double Roman Domination Number of Graphs.
International Journal of Mathematical and Computer SciencesIn this paper, we establish sharp upper and lower bounds for this parameter. These results provide the first systematic study of hop double Roman domination and lay the foundation for future investigations into its structural and computational aspects.
Jamil J. Hamja +6 more
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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 ...
Shailaja S. Shirkol +2 more
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