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Total Version of the Domination Game [PDF]
Graphs and Combinatorics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Henning +2 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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On the Total k-Domination in Graphs
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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On the total domination number of total graphs
Discussiones Mathematicae Graph TheorySummary: Let \(G\) be a graph with no isolated vertex. A set \(D\subseteq V(G)\) is a total dominating set of \(G\) if every vertex of \(G\) is adjacent to at least one vertex in \(D\). The total domination number of \(G\), denoted by \(\gamma_t(G)\), is the minimum cardinality among all total dominating sets of \(G\).
Abel Cabrera-Martínez +2 more
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A Cross-Entropy Approach to the Domination Problem and Its Variants [PDF]
EntropyThe domination problem and three of its variants (total domination, 2-domination, and secure domination) are considered. These problems have various real-world applications, including error correction codes, ad hoc routing for wireless networks, and ...
Ryan Burdett +2 more
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Total Domination Versus Paired-Domination in Regular Graphs
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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On the domination of triangulated discs [PDF]
Mathematica Bohemica, 2023 Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac14(n+2)$.
Noor A'lawiah Abd Aziz +2 more
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Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 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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On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
Abel Cabrera Martínez +2 more
doaj +1 more source