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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
Silvia Bianchi, Annegret K Wagler
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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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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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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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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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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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Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths
International Journal of Mathematics Trends and Technology, 2014Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets in G with cardinality i. The polynomial Dct (G, x) = n i (G) ct dct (G, i) x is called the connected total domination polynomial of G. In this paper, we obtain a recursive formula for dct ( 2 n P , i).
A Vijayan, T. Anitha Baby
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