Results 51 to 60 of about 10,021,129 (363)
Graphs and CombinatoricsLet G be a bridgeless graph. An orientation of G is a digraph obtained from G by assigning a direction to each edge. The oriented diameter of G is the minimum diameter among all strong orientations of G.
P. Dankelmann +2 more
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Resolving domination number of helm graph and it’s operation
Journal of Physics: Conference Series, 2020 Let G be a connected graph. Dominating set is a set of vertices which each vertex D has at least one neighbor in G. The minimum cardinality of D is called the domination number G(γ(G)).
A. N. Hayyu +4 more
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Characterization of Upper Detour Monophonic Domination Number
Cubo, 2020 This paper introduces the concept of \textit{upper detour monophonic domination number} of a graph. For a connected graph $G$ with vertex set $V(G)$, a set $M\subseteq V(G)$ is called minimal detour monophonic dominating set, if no proper subset of $M ...
M. Mohammed Abdul Khayyoom
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Graphs with equal domination and certified domination numbers [PDF]
Opuscula Mathematica, 2019 A set \(D\) of vertices of a graph \(G=(V_G,E_G)\) is a dominating set of \(G\) if every vertex in \(V_G-D\) is adjacent to at least one vertex in \(D\). The domination number (upper domination number, respectively) of \(G\), denoted by \(\gamma(G)\) (\(\Gamma(G)\), respectively), is the cardinality of a smallest (largest minimal, respectively ...
Magda Dettlaff +5 more
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The 3-Rainbow Domination Number of the Cartesian Product of Cycles
Mathematics, 2020 We have studied the k-rainbow domination number of C n □ C m for k ≥ 4 (Gao et al. 2019), in which we present the 3-rainbow domination number of C n □ C m , which should be bounded above by the four-rainbow domination number of C n □ C m .
Hong Gao, Changqing Xi, Yuansheng Yang
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Discrete Mathematics, 2002 The dominating set of a digraph \(D\) is a set \(S\) of vertices such that for every \(v\not\in S\) there exists \(u\in S\) with \(uv\in A(D)\). The domination number of \(D\) is the cardinality of the smallest dominating set. The game domination number of an undirected graph \(G\) is the domination number of the digraph \(D\) obtained as a result of ...
Alon, Noga +3 more
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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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Total Roman Domination Number of Rooted Product Graphs
, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
A. Cabrera Martínez +3 more
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Alternative Domination in Graphs
AKCE International Journal of Graphs and CombinatoricsSometimes while you are using the Internet, for example, via a Wi-Fi network from one of the companies, the Internet is suddenly cut off due to a malfunction at that point, which disrupts your important work on the Internet, so there is a need for ...
Ali Mohammed Sahal
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On the Outer Independent Double Roman Domination Number [PDF]
Bulletin of the Iranian Mathematical Society, 2019 An outer independent (double) Roman dominating function is a (double) Roman dominating function f for which the set of vertices assigned 0 under f is independent.
D. Mojdeh +3 more
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