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Polyhedra associated with locating-dominating, open locating-dominating and locating total-dominating sets in graphs [PDF]
Discrete Applied Mathematics, 2022 International audienceThe problems of determining locating-dominating, open locating-dominating or locating total-dominating sets of minimum cardinality in a graph G are variations of the classical minimum dominating set problem in G and are all known to
Annegret Wagler, Silvia Bianchi
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Total Dominating Sets in Maximal Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2017 A set \(D\subseteq V(G)\) is a total domination set of graph \(G\) if every vertex from \(V(G)\) has a neighbor in \(D\). The minimum cardinality of a total domination set of \(G\) is called total domination number and is denoted by \(\gamma_t(G)\). A recent result from \textit{M. Dorfling} et al. [Discrete Math. 339, No.
Magdalena Lemanska +2 more
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Graphs with few total dominating sets
Discrete Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcin Krzywkowski, Stephan G. Wagner
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INTERIOR TOTAL DOMINATING SETS IN GRAPHS
Advances and Applications in Discrete Mathematics, 2018Summary: Let \(G = (V(G)\), \(E(G))\) be a simple graph. A total dominating set \(D\) of \(V(G)\) is an interior total dominating set of \(G\) if every \(v\in D\) is an interior vertex of \(G\). The minimum cardinality of an interior total dominating set of \(G\), denoted by \(\gamma_{lt}(G)\) is called an interior total domination number of \(G\).
Pacardo, Shiela Mae B., Rara, Helen M.
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2005
In this paper, we consider cooperative games arising from total domination problem on graphs. We introduce two games, rigid total dominating set game and relaxed total dominating set game, and focus on their cores. First, a common necessary and sufficient condition for the balancedness of the two total dominating set games is obtained.
Qizhi Fang, Hye Kyung Kim, Dae Sik Lee
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In this paper, we consider cooperative games arising from total domination problem on graphs. We introduce two games, rigid total dominating set game and relaxed total dominating set game, and focus on their cores. First, a common necessary and sufficient condition for the balancedness of the two total dominating set games is obtained.
Qizhi Fang, Hye Kyung Kim, Dae Sik Lee
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On the Number of Minimum Total Dominating Sets in Trees
Journal of Applied and Industrial Mathematics, 2023Summary: The minimum total dominating set (MTDS) of a graph is a vertex subset \(D\) of minimum cardinality such that every vertex of the graph is adjacent to at least one vertex of \(D\). In this paper we obtain the sharp upper bound for the number of MTDS in the class of \(n\)-vertex 2-caterpillars.
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Information Processing Letters, 2012
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Oliver Schaudt, Rainer Schrader
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Oliver Schaudt, Rainer Schrader
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Approximation for minimum total dominating set
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human, 2009A total dominating set is a dominating set which induces a subgraph without isolated vertices. In this paper, we study the approximation of minimum total dominating set problem. First, we present a new analysis for one-step greedy algorithm with approximation ratio ln(δ-0.5)+1.5, where δ is the maximum degree of the given graph.
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Linear Separation of Total Dominating Sets in Graphs
2013A total dominating set in a graph is a set of vertices such that every vertex of the graph has a neighbor in the set. We introduce and study graphs that admit non-negative real weights associated to their vertices so that a set of vertices is a total dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We show
Nina Chiarelli, Martin Milanic
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Algorithmic results in secure total dominating sets on graphs
Theoretical Computer Science, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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