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Quaestiones Mathematicae, 2017
A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. A dominating set S of D is called a total dominating set of D if the subdigraph of D induced by S has no isolated vertices.
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A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. A dominating set S of D is called a total dominating set of D if the subdigraph of D induced by S has no isolated vertices.
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A note on domination and total domination in prisms
Journal of Combinatorial Optimization, 2017Recently, Azarija et al. (Electron J Combin:1.19, 2017) considered the prism $$G \mathop {\square }K_2$$ of a graph G and showed that
Wayne Goddard +2 more
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2021
Total domination is the second most studied topic in domination theory, and thus the total domination game is a natural variation of the domination game. It was introduced and first studied in 2015 by Henning, Klavžar, and Rall. There are, of course, some similarities between these two kinds of domination games, but it was shown in this introductory ...
Michael A. Henning +3 more
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Total domination is the second most studied topic in domination theory, and thus the total domination game is a natural variation of the domination game. It was introduced and first studied in 2015 by Henning, Klavžar, and Rall. There are, of course, some similarities between these two kinds of domination games, but it was shown in this introductory ...
Michael A. Henning +3 more
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Dominator and Total Dominator Colorings in Graphs
2021A dominator coloring of a graph G is a proper coloring of the vertices of G in which each vertex of the graph dominates every vertex of some color class, where a vertex dominates itself and all vertices adjacent to it. The dominator chromatic number of G is the minimum number of colors among all dominator coloring of G.
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Total domination and transformation
Information Processing Letters, 1997Abstract Using a linear time many-one reduction from the problem total dominating set to the problem dominating set we show how to obtain efficient algorithms to compute a minimum cardinality total dominating set on a variety of graph classes, among them permutation graphs, dually chordal graphs and k -polygon graphs.
Lorna Stewart, Dieter Kratsch
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Variations of Total Domination
2013In the metadata of the chapter that will be visualized online, please replace the abstract with the following: “In this chapter, we consider four variations of a total dominating set in a graph and briefly discuss each variation.”
Michael A. Henning, Anders Yeo
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2013
In this chapter we focus on the upper total domination number of a graph. Recall that the upper domination number of a graph G, denoted by Γ(G), is the maximum cardinality of a minimal dominating set in G, while the upper total domination number of G, denoted by Γ t (G), is the maximum cardinality of a minimal TD-set in G.
Anders Yeo, Michael A. Henning
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In this chapter we focus on the upper total domination number of a graph. Recall that the upper domination number of a graph G, denoted by Γ(G), is the maximum cardinality of a minimal dominating set in G, while the upper total domination number of G, denoted by Γ t (G), is the maximum cardinality of a minimal TD-set in G.
Anders Yeo, Michael A. Henning
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2013
In this chapter, we present results on total domination in trees. For a linear algorithm to compute the total domination of a tree, see Sect. 3.5.
Michael A. Henning, Anders Yeo
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In this chapter, we present results on total domination in trees. For a linear algorithm to compute the total domination of a tree, see Sect. 3.5.
Michael A. Henning, Anders Yeo
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Total domination in block graphs
Operations Research Letters, 1989A set of vertices D is a total dominating set for a graph G if every vertex of G is adjacent with at least one vertex in D. Although the problem of determining the minimum cardinality of a total dominating set for an arbitrary graph is NP-complete, polynomial time algorithm are known for certain classes of graphs (e.g. trees, interval graphs).
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Total domination in interval graphs
Information Processing Letters, 1986A set of vertices D is a total dominating set for a graph \(G=(V,E)\) if every vertex in V is adjacent to a vertex in D. An interval graph is the intersection graph of intervals of the real line. This paper presents an \(O(| V| +| E|)\) time algorithm for the problem of finding the minimum cardinality total dominating set in an interval graph.
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