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Independent double Roman domination in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 For a graph G = (V,E), a double Roman dominating function has the property that for every vertex with f(v) = 0, either there exists a vertex , with f(u) = 3, or at least two neighbors having f(x) = f(y) = 2, and every vertex with value 1 under f has at ...
H. R. Maimani +3 more
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On the Outer-Independent Double Roman Domination of Graphs [PDF]
Frontiers in Applied Mathematics and Statistics, 2021 An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex ...
Yongsheng Rao +4 more
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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 +3 more
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On the Outer Independent Total Double Roman Domination in Graphs [PDF]
Mediterranean Journal of Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Abdollahzadeh Ahangar +3 more
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Lower and upper bounds on independent double Roman domination in trees [PDF]
Electronic Journal of Graph Theory and Applications, 2022 Summary: For a graph \(G = (V, E)\), a double Roman dominating function (DRDF) \(f : V \rightarrow \{0, 1, 2, 3\}\) has the property that for every vertex \(v\in V\) with \(f(v)=0\), either there exists a neighbor \(u \in N(v)\), with \(f(u)=3\), or at least two neighbors \(x, y \in N(v)\) having \(f(x)=f(y)=2\), and every vertex with value 1 under \(f\
M. Kheibari +3 more
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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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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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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
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Outer independent double Roman domination number of graphs [PDF]
, 2019 A double Roman dominating function of a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2,3\}$ having the property that for each vertex $v$ with $f(v)=0$, there exists $u\in N(v)$ with $f(u)=3$, or there are $u,w\in N(v)$ with $f(u)=f(w)=2$, and if $f(v)=1$, then $v$ is adjacent to a vertex assigned at least $2$ under $f$.
Doost Ali Mojdeh +3 more
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Independent Double Roman Domination on Block Graphs [PDF]
, 2019 Given a graph $G=(V,E)$, $f:V \rightarrow \{0,1,2 \}$ is the Italian dominating function of $G$ if $f$ satisfies $\sum_{u \in N(v)}f(u) \geq 2$ when $f(v)=0$. Denote $w(f)=\sum_{v \in V}f(v)$ as the weight of $f$. Let $V_i=\{v:f(v)=i\},i=0,1,2$, we call $f$ the independent Italian dominating function if $V_1 \cup V_2$ is an independent set.
Decheng Wei, Changhong Lü
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