On the Game Total Domination Number
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DOI: 10.1007/s00373-018-1883-y
Abstract: The total domination game is a two-person competitive optimization game, where the players, Dominator and Staller, alternately select vertices of an isolate-free graph G. Each vertex chosen must strictly increase the number of vertices totally… read more here.
Keywords: game; domination number; game total; total domination ... See more keywords
On two conjectures concerning total domination subdivision number in graphs
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DOI: 10.1007/s10878-019-00383-4
Abstract: A subset S of vertices of a graph G without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number$$\gamma _t(G)$$γt(G) is… read more here.
Keywords: two conjectures; number; subdivision number; total domination ... See more keywords
Total k-domination in Cartesian product graphs
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DOI: 10.1007/s10998-017-0191-2
Abstract: Let $$G=(V,E)$$G=(V,E) be a graph. A set $$S\subseteq V$$S⊆V is a total k-dominating set if every vertex $$v\in V$$v∈V has at least k neighbors in S. The total k-domination number $$\gamma _{kt}(G)$$γkt(G) is the minimum… read more here.
Keywords: domination; total domination; domination number; cartesian product ... See more keywords
Infinite Families of Circular and Möbius Ladders that are Total Domination Game Critical
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-018-0635-8
Abstract: Let $$\gamma _\mathrm{tg}(G)$$γtg(G) denote the game total domination number of a graph G, and let G|v mean that a vertex v of G is declared to be already totally dominated. A graph G is total… read more here.
Keywords: total domination; gamma mathrm; gamma; game ... See more keywords
Locating-Total Domination in Grid Graphs
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DOI: 10.1007/s40840-019-00733-9
Abstract: Let $$G=(V,E)$$ G = ( V , E ) be a graph with no isolated vertex. A subset $$S\subseteq V(G)$$ S ⊆ V ( G ) is a total dominating set of graph G if… read more here.
Keywords: total domination; locating total; dominating set; total dominating ... See more keywords
On the sum of the total domination numbers of a digraph and its converse
Sign Up to like & getrecommendations! Published in 2019 at "Quaestiones Mathematicae"
DOI: 10.2989/16073606.2018.1438531
Abstract: Abstract A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S has an in-neighbor in S. A dominating set S of D is called… read more here.
Keywords: domination numbers; converse; total domination; dominating set ... See more keywords
Total Domination in Rooted Product Graphs
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DOI: 10.3390/sym12111929
Abstract: During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the… read more here.
Keywords: total domination; product; product graphs; domination ... See more keywords