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Double Roman domination number
Discrete Applied Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anu V., Aparna Lakshmanan S.
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Vertex-edge perfect Roman domination number
AIMS Mathematics, 2023 <abstract><p>A vertex-edge perfect Roman dominating function on a graph $ G = (V, E) $ (denoted by ve-PRDF) is a function $ f:V\left(G\right)\longrightarrow\{0, 1, 2\} $ such that for every edge $ uv\in E $, $ \max\{f(u), f(v)\}\neq0 $, or $ u $ is adjacent to exactly one neighbor $ w $ such that $ f(w) = 2 $, or $ v $ is adjacent to ...
Bana Al Subaiei +2 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 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. +2 more
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Trees with vertex-edge Roman Domination number twice the domination number minus one
Proyecciones (Antofagasta), 2020 A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices.
H. Naresh Kumar, Y. B. Venkatakrishnan
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AKCE International Journal of Graphs and Combinatorics, 2022 H. Abdollahzadeh Ahangar
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Twin Roman domination number of a digraph [PDF]
Miskolc Mathematical Notes, 2016 Abdollahzadeh Ahangar, Hossein +4 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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On a Vizing-type integer domination conjecture [PDF]
, 2020 Given a simple graph $G$, a dominating set in $G$ is a set of vertices $S$ such that every vertex not in $S$ has a neighbor in $S$. Denote the domination number, which is the size of any minimum dominating set of $G$, by $\gamma(G)$.
Davila, Randy, Krop, Elliot
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AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple graph with vertex set $ V $ and edge set $ E $, and let $ f $ be a function $ f:V\mapsto \{0, 1, 2\} $. A vertex $ u $ with $ f(u) = 0 $ is said to be undefended with respect to $ f $ if it is not adjacent to a vertex with ...
Jian Yang, Yuefen Chen, Zhiqiang Li
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The Perfect Roman Domination Number of the Cartesian Product of Some Graphs
Journal of mathematics, 2022 A perfect Roman dominating function on a graph G is a function f : V(G)⟶{0,1,2} for which every vertex v with f(v) = 0 is adjacent to exactly one neighbor u with f(u) = 2. The weight of f is the sum of the weights of the vertices.
Ahlam Almulhim, A. Akwu, Bana Al Subaiei
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