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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 ...
Boštjan Brešar +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 ...
Boštjan Brešar +3 more
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Total Dominator Colorings and Total Domination in Graphs
Graphs and Combinatorics, 2014Given a graph \(G\), a total dominator coloring is a proper coloring of the vertices of \(G\) in which each vertex is adjacent to every vertex of some color class. The total dominator chromatic number \(\chi_{d}^{t}(G)\) of \(G\) is the minimum number of colors among all total dominator colorings of \(G\). A total dominating set of \(G\) is a set \(S\)
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Total Domination Edge Critical Graphs with Total Domination Number Three and Many Dominating Pairs
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Balbuena, Camino +3 more
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Domination and Total Domination in Hypergraphs
2020A dominating set in a hypergraph H with vertex set V (H) and E(H) is a subset of vertices D ⊆ V (H) such that for every vertex v ∈ V (H) ∖ D, there exists an edge e ∈ E(H) for which v ∈ e and e ∩ D≠∅. A total dominating set in H is a dominating set D of H with the additional property that for every vertex v in D, there exists an edge e ∈ E(H) for which
Henning, Michael A., Yeo, Anders
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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.
Michael A. Henning, Anders Yeo
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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.
Michael A. Henning, Anders Yeo
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Total forcing versus total domination in cubic graphs
Applied Mathematics and Computation, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Randy Davila, Michael A. Henning
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SUPERLATIVE TOTAL DOMINATION IN GRAPHS
Electronic Journal of Mathematical Analysis and ApplicationsSummary: Let \(G= (V, E)\) be a simple graph with no isolated vertices and \(p \geq 3\). A set \(D \subseteq V\) is a dominating set, abbreviated as DS, of a graph \(G\), if every vertex in \(V-D\) is adjacent to some vertex in \(D\), while a total dominating set, abbreviated as TDS, of \(G\) is a set \(T \subseteq V\) such that every vertex in \(G ...
Bankapur, Veena, Chaluvaraju, B.
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Total Dominator Total Chromatic Numbers of Some Graphs
Utilitas MathematicaTotal dominator total coloring of a graph is a total coloring of the graph such that each object of the graph is adjacent or incident to every object of some color class. The minimum namber of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph.
Vusuqi, Leila +2 more
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Total domination edge critical graphs
1998A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called total dominating in \(G\), if for each \(x\in V(G)\) there exists a vertex \(y\in D\) adjacent to \(x\). The minimum number of vertices of a total dominating set in \(G\) is the total domination number \(\gamma_t(G)\) of \(G\).
Van Der Merwe, L. C. +2 more
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