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On the Total k-Domination in Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2018 Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets.
Bermudo Sergio +2 more
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Total Domination Versus Paired-Domination in Regular Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
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A note on total domination [PDF]
Discrete Mathematics, 1984 A dominating [totally dominating] set is a subset D of the vertex set V(G) of a graph G with the property that for each \(x\in V(G)\setminus D\) [for each \(x\in V(G)]\) there exists \(y\in D\) adjacent to x. The domination number \(\gamma\) (G) [the total domination number \(\gamma_ t(G)]\) of G is the minimum number of vertices of a dominating ...
Robert B. Allan +2 more
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Total Domination Multisubdivision Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Total and Double Total Domination on Octagonal Grid
AxiomsA k-total dominating set is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves, have at least k neighbors in the dominating set.
Antoaneta Klobučar +1 more
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Bounds on Global Total Domination in Graphs [PDF]
Computer Science Journal of Moldova, 2015 A subset $S$ of vertices in a graph $G$ is a \textit{global total dominating set}, or just GTDS, if $S$ is a \textit{total dominating set} of both $G$ and $\overline{G}$.
Nader Jafari Rad, Elahe Sharifi
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RAIRO - Theoretical Informatics and Applications, 2020 An edge e ev-dominates a vertex v which is a vertex of e, as well as every vertex adjacent to v. A subset D ⊆ E is an edge-vertex dominating set (in simply, ev-dominating set) of G, if every vertex of a graph G is ev-dominated by at least one edge of D.
Sahin, Abdulgani +5 more
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Domination and Total Domination in Hypergraphs
, 2020 A dominating set in a hypergraph H with vertex set V (H) and E(H) is a subset of vertices D ⊆ V (H) such that for every vertex v ∈ V (H) ∖ D, there exists an edge e ∈ E(H) for which v ∈ e and e ∩ D≠∅. A total dominating set in H is a dominating set D of H with the additional property that for every vertex v in D, there exists an edge e ∈ E(H) for which
Henning, Michael A., Yeo, Anders
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Domination and total domination in complementary prisms
Journal of Combinatorial Optimization, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teresa W. Haynes +2 more
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Partial Total Domination in Hypergraphs
MathematicsThis paper establishes fundamental results for partial total domination in hypergraphs. We present tight bounds for the partial total domination number in k-uniform hypergraphs, demonstrate relationships with classical domination parameters, and provide ...
Abdulkafi Sanad, Chaoqian Li
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