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Maker-Breaker total domination game [PDF]
Discrete Applied Mathematics, 2019 Maker-Breaker total domination game in graphs is introduced as a natural counterpart to the Maker-Breaker domination game recently studied by Duch\^ene, Gledel, Parreau, and Renault. Both games are instances of the combinatorial Maker-Breaker games.
Gledel, Valentin +3 more
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Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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Graphs with Large Disjunctive Total Domination Number [PDF]
, 2014 Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $\gamma_t(G)$.
Henning, Michael A., Naicker, Viroshan
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Disjunctive Total Domination in Graphs [PDF]
Journal of Combinatorial Optimization, 2014 Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $\gamma_t(G)$.
Henning, Michael A., Naicker, Viroshan
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Signed total Italian k-domination in graphs [PDF]
, 2021 Published by Azabaijan Shahid Madani University, Azarshahr ...
Lutz Volkmann
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On Total Vertex-Edge Domination [PDF]
, 2018 A novel domination invariant defined by Boutrig and Chellali in the recent: total vertex-edge domination. In this paper we obtain an improved upper bound of total vertex edge-domination number of a tree. If is a connected tree with order , then with and we characterize the trees attaining this upper bound.
Bünyamin Şahin, Abdulgani Şahi̇n
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Total Domination Multisubdivision Number of a Graph
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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A Cross-Entropy Approach to the Domination Problem and Its Variants [PDF]
EntropyThe domination problem and three of its variants (total domination, 2-domination, and secure domination) are considered. These problems have various real-world applications, including error correction codes, ad hoc routing for wireless networks, and ...
Ryan Burdett +2 more
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Total Dominating Sequences in Graphs
Discrete Mathematics, 2016 A vertex in a graph totally dominates another vertex if they are adjacent. A sequence of vertices in a graph $G$ is called a total dominating sequence if every vertex $v$ in the sequence totally dominates at least one vertex that was not totally ...
Bresar, Bostjan +2 more
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