Results 51 to 60 of about 9,423,140 (336)
On resolving domination number of friendship graph and its operation
Journal of Physics: Conference Series, 2020 Let G = (V, E) be a simple, finite, and connected graph of order n. A dominating set D ⊆ V(G) such every vertex not in D is adjacent to at least one member of D.
S. Kurniawati +4 more
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All graphs with paired-domination number two less than their order [PDF]
Opuscula Mathematica, 2013 Let \(G=(V,E)\) be a graph with no isolated vertices. A set \(S\subseteq V\) is a paired-dominating set of \(G\) if every vertex not in \(S\) is adjacent with some vertex in \(S\) and the subgraph induced by \(S\) contains a perfect matching.
Włodzimierz Ulatowski
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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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New Results in Bi- Domination in Graphs
Zanco Journal of Pure and Applied Sciences, 2022 In this paper, some new results are introduced for the bi-domination in graphs. Some properties of bi-domination number and bounds according to maximum, minimum degrees, order, and size have been determined.
M. N. Al-Harere , Athraa T. Breesam
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A note on the bounds of Roman domination numbers
AIMS Mathematics, 2021 Let $G$ be a graph and $f: V(G) \rightarrow \{0,1,2\}$ be a mapping. $f$ is said to be a Roman dominating function of $G$ if every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Zepeng Li
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Changing and Unchanging of the Domination Number of a Graph: Path Addition Numbers [PDF]
Discussiones Mathematicae Graph Theory, 2018 Given a graph G =(V, E) and two its distinct vertices u and v, the (u, v)-Pk-addition graph of G is the graph Gu,v,k−2 obtained from disjoint union of G and a path Pk : x0, x1,...,xk−1, k ≥ 2, by identifying the vertices u and x0, and identifying the ...
V. Samodivkin
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On the ratio of the domination number and the independent domination number in graphs
Discrete Applied Mathematics, 2014 Abstract We let γ ( G ) and i ( G ) denote the domination number and the independent domination number of G , respectively. Recently, Rad and Volkmann conjectured that i ( G ) / γ ( G ) ≤ Δ ( G ) / 2 for every graph G , where Δ ( G ) is the maximum degree of G .
Akinari Sasaki +2 more
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On the strength and domination number of graphs
Contributions to Mathematics, 2023 A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\left\{ 1,2,\ldots ,n\right\} $ to the vertices of $G$. The strength $\textrm{str}_{f}\left( G\right)$ of a numbering $f:V\left( G\right) \rightarrow \left\{ 1,2,\ldots ,n\right\} $ of $G$ is defined by% \begin{equation*} \mathrm{str}_{f}\left( G\right)
Yukio Takahashi +2 more
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Domination Number of Graphs with Minimum Degree Five [PDF]
Discussiones Mathematicae Graph Theory, 2019 We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method.
Csilla Bujt'as
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Results on the domination number and the total domination number of Lucas cubes
Ars Mathematica Contemporanea, 2020 Lucas cubes are special subgraphs of Fibonacci cubes. For small dimensions, their domination numbers are obtained by direct search or integer linear programming. For larger dimensions some bounds on these numbers are given. In this work, we present the exact values of total domination number of small dimensional Lucas cubes and present optimization ...
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