Results 21 to 30 of about 398,878 (275)
Some results on the open locating-total domination number in graphs [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we generalize the concept of an open locating-dominating set in graphs. We introduce a concept as an open locating-total dominating set in graphs that is equivalent to the open neighborhood locating-dominating set.
Fateme Movahedi, Mohammad Hadi Akhbari
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More on the Enumeration of Some Kind of Dominating Sets in Cactus Chains [PDF]
Mathematics Interdisciplinary Research, 2022 A non-empty set S ⊆ V is a dominating set, if every vertex not in S is adjacent to at least one vertex in S, and S is a total dominating set, if every vertex of V is adjacent to some vertices of S.
Somayeh Jahari, Saeid Alikhani
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Disjoint total dominating sets in near‐triangulations
Journal of Graph Theory, 2023 AbstractWe show that every simple planar near‐triangulation with minimum degree at least three contains two disjoint total dominating sets. The class includes all simple planar triangulations other than the triangle. This affirms a conjecture of Goddard and Henning.
P. Francis +3 more
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A linear-time algorithm to compute total $[1,2]$-domination number of block graphs [PDF]
AUT Journal of Mathematics and Computing, 2020 Let $G=(V, E)$ be a simple graph without isolated vertices. A set $D\subseteq V$ is a total $[1,2]$-dominating set if for every vertex $v\in V , 1\leq |N(v)\cap D|\leq 2$.
Pouyeh Sharifani +2 more
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Nordhaus-Gaddum bounds for upper total domination [PDF]
Opuscula Mathematica, 2022 A set \(S\) of vertices in an isolate-free graph \(G\) is a total dominating set if every vertex in \(G\) is adjacent to a vertex in \(S\). A total dominating set of \(G\) is minimal if it contains no total dominating set of \(G\) as a proper subset. The
Teresa W. Haynes, Michael A. Henning
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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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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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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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