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Quaestiones Mathematicae, 2015
A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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Total domination and transformation
Information Processing Letters, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dieter Kratsch, Lorna Stewart
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Networks, 1980
AbstractA set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating ...
Ernest J. Cockayne +2 more
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AbstractA set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating ...
Ernest J. Cockayne +2 more
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A note on domination and total domination in prisms
Journal of Combinatorial Optimization, 2017Let \(G=(V,E)\) be a simple graph. A subset \(S \subseteq V\) is a dominating set if every vertex \(v \in V\setminus S\) is adjacent to a vertex in S. The minimum cardinality of a dominating set, denoted by \(\gamma(G)\), called the domination number of graph \(G\).
Wayne Goddard, Michael A. Henning
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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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Domination and total domination in complementary prisms
Journal of Combinatorial Optimization, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teresa W. Haynes +2 more
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Girth and Total Domination in Graphs
Graphs and Combinatorics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael A. Henning, Anders Yeo
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On double edge-domination and total domination of trees
Journal of Intelligent & Fuzzy Systems, 2021In a graph G, a vertex v is dominated by an edge e, if e is incident with v or e is incident with a vertex which is a neighbor of v. An edge-vertex dominating set D is a subset of the edge set of G such that every vertex of G is edge-vertex dominated by an edge of D.
Sahin, Bunyamin +5 more
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Relating the total \(\{2\}\)-domination number with the total domination number of graphs
Discret. Appl. Math., 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismael Ríos Villamar +3 more
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Ars Comb., 1996
A total dominating set in a graph \(G\) is a subset \(D\) of the vertex set \(V(G)\) of \(G\) with the property that for each vertex \(x\in V(G)\) 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 \(G.\) The symbol \(\overline G ...
S. Arumugam, A. Thuraiswamy
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A total dominating set in a graph \(G\) is a subset \(D\) of the vertex set \(V(G)\) of \(G\) with the property that for each vertex \(x\in V(G)\) 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 \(G.\) The symbol \(\overline G ...
S. Arumugam, A. Thuraiswamy
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