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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 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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A Characterization of Graphs with Disjoint Dominating and Total Dominating Sets
Quaestiones Mathematicae, 2009A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this paper, we provide a constructive characterization of graphs whose vertex set can be partitioned into a ...
Henning, Michael A, Southey, Justin
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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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Graphs with Disjoint Total Dominating Sets
2013In the metadata of the chapter that will be visualized online, please replace the abstract with the following: “A classical result in domination theory is that the vertex set of every graph without isolates can be partitioned into two dominating sets.
Michael A. Henning, Anders Yeo
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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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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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Approximation algorithms for the total dominating set problem
Journal of Combinatorial OptimizationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Limin Wang +4 more
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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 Milanič
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