Results 11 to 20 of about 9,917,456 (366)
The Domination Number of Grids [PDF]
SIAM Journal on Discrete Mathematics, 2011 In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 ...
Alexandre Pinlou +9 more
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On the $ \{2\} $-domination number of graphs
AIMS Mathematics, 2022 Let $ G $ be a nontrivial graph and $ k\geq 1 $ an integer. Given a vector of nonnegative integers $ w = (w_0, \ldots, w_k) $, a function $ f: V(G)\rightarrow \{0, \ldots, k\} $ is a $ w $-dominating function on $ G $ if $ f(N(v))\geq w_i $ for every $ v\
A. Cabrera-Martínez, A. C. Peiró
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Graphs with equal domination and independent domination numbers [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Let γ(G) and i(G) denote the domination number and independent domination number of a graph G. In this article, we establish a sufficient condition for a graph G to satisfy which yields some of the well known classical theorems as corollaries.
Purnima Gupta, Rajesh Singh, S. Arumugam
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On Domination Number and Distance in Graphs [PDF]
Discrete Applied Mathematics, 2014 A vertex set $S$ of a graph $G$ is a \emph{dominating set} if each vertex of $G$ either belongs to $S$ or is adjacent to a vertex in $S$. The \emph{domination number} $\gamma(G)$ of $G$ is the minimum cardinality of $S$ as $S$ varies over all dominating ...
Kang, Cong X.
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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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On the equality of domination number and 2-domination number
Discussiones Mathematicae Graph TheoryThe 2-domination number $ _2(G)$ of a graph $G$ is the minimum cardinality of a set $ D \subseteq V(G) $ for which every vertex outside $ D $ is adjacent to at least two vertices in $ D $. Clearly, $ _2(G) $ cannot be smaller than the domination number $ (G) $. We consider a large class of graphs and characterize those members which satisfy $ _2=
Gülnaz Boruzanlı Ekinci +1 more
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The difference between the domination number and the minus domination number of a cubic graph
Applied Mathematics Letters, 2003 The paper concerns the domination number and the minus domination number of a graph. Let \(G\) be an undirected graph with vertex set \(V\). For each \(v\in V\) the symbol \(N[v]\) denotes the closed neighbourhood of \(v\) in \(G\), i.e. the set consisting of \(v\) and of all vertices adjacent to \(v\) in \(G\).
Xiaofan Yang +3 more
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Medium Domination Decomposition of Graphs
Ratio Mathematica, 2022 A set of vertices in a graph dominates if every vertex in is either in or adjacent to a vertex in . The size of any smallest dominating set is called domination number of .
E Ebin Raja Merly, Saranya J
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On the domination search number [PDF]
Discrete Applied Mathematics, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dieter Kratsch +2 more
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Further results on the total Italian domination number of trees
AIMS Mathematics, 2023 Let $ f:V(G)\rightarrow \{0, 1, 2\} $ be a function defined from a connected graph $ G $. Let $ W_i = \{x\in V(G): f(x) = i\} $ for every $ i\in \{0, 1, 2\} $. The function $ f $ is called a total Italian dominating function on $ G $ if $ \sum_{v\in N(x)}
Abel Cabrera-Martínez +2 more
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