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The Electronic Journal of Combinatorics, 2017 Using hypergraph transversals it is proved that $\gamma_t(Q_{n+1}) = 2\gamma(Q_n)$, where $\gamma_t(G)$ and $\gamma(G)$ denote the total domination number and the domination number of $G$, respectively, and $Q_n$ is the $n$-dimensional hypercube. More generally, it is shown that if $G$ is a bipartite graph, then $\gamma_t(G \square K_2) = 2\gamma(G ...
Azarija, Jernej +2 more
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Total Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σu∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x ∈ V (G) : f(x) = i}. A total dominating
Martínez Abel Cabrera +1 more
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Trees with equal total domination and game total domination numbers
Discrete Applied Mathematics, 2017 23 pages, 5 figures, 22 ...
Henning, Michael A., Rall, Douglas F.
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Total domination versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2012 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by t.
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Equality of total domination and chromatic total domination in graphs
International journal of health sciences, 2022 Let be a simple, finite and undirected graph and without isolated vertex. A subset D of V is said to be dominating set if for every in there exist a vertex in such that and are adjacent. The minimum cardinality of a dominating set of is called the domination number of and is denoted by .
M. Angala Eswari, S. Balamurugan
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Jambura Journal of Mathematics, 2022 Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G).
Nurhamzah Nurhamzah +2 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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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
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Total [1,2]-domination in Graphs
Acta Mathematicae Applicatae Sinica, English Series, 2018 17 ...
Lv, Xue-Zheng, Wu, Baoyindureng
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Total Domination in Partitioned Graphs [PDF]
Graphs and Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Frendrup, Allan +2 more
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