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Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree
Discussiones Mathematicae Graph Theory, 2016 Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters; namely, the domination number, γ(G), and the total domination number, γt(G). A set S of vertices
Henning Michael A., Marcon Alister J.
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Bounds on the Locating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2020 Given a graph G = (V, E) with no isolated vertex, a subset S of V is called a total dominating set of G if every vertex in V has a neighbor in S. A total dominating set S is called a locating-total dominating set if for each pair of distinct vertices u ...
Wang Kun, Ning Wenjie, Lu Mei
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Some results on domination in annihilating-ideal graphs of commutative rings [PDF]
Journal of Hyperstructures. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are ...
Reza Taheri
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On Two Open Problems on Double Vertex-Edge Domination in Graphs
Mathematics, 2019 A vertex v of a graph G = ( V , E ) , ve-dominates every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a double vertex-edge dominating set if every edge of E is ve-dominated by at least two
Fang Miao +5 more
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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Total Italian domatic number of graphs [PDF]
Computer Science Journal of Moldova, 2023 Let $G$ be a graph with vertex set $V(G)$. An \textit{Italian dominating function} (IDF) on a graph $G$ is a function $f:V(G)\longrightarrow \{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to a vertex $u$ with $f(u)=2$ or to two ...
Seyed Mahmoud Sheikholeslami +1 more
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An introduction of total dominator color class total dominating sets in graphs
Malaya Journal of Matematik, 2021 Let $G$ be a finite, undirected and connected graph with minimum degree at least one. In this paper we define a new graph parameter called total dominator color class total domination number of $G$. A proper coloring $\mathcal{C}$ of $G$ is said to be a total dominator color class total dominating set of $G$ if each vertex properly dominates a color ...
null A. Vijayalekshmi, null S. Abisha
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A Note on the Locating-Total Domination in Graphs
Discussiones Mathematicae Graph Theory, 2017 In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Miller Mirka +4 more
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Fair Total Domination Number in Cactus Graphs
Discussiones Mathematicae Graph Theory, 2021 For k ≥ 1, a k-fair total dominating set (or just kFTD-set) in a graph G is a total dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V\S. The k-fair total domination number of G, denoted by ftdk(G), is the minimum cardinality of a kFTD-set.
Hajian Majid, Rad Nader Jafari
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Blocking total dominating sets via edge contractions
Theoretical Computer Science, 2021 In this paper, we study the problem of deciding whether the total domination number of a given graph $G$ can be reduced using exactly one edge contraction (called 1-Edge Contraction($γ_t$)). We focus on several graph classes and determine the computational complexity of this problem.
Esther Galby, Felix Mann, Bernard Ries
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