
[1,2]Domination in Generalized Petersen Graphs
A vertex subset S of a graph G=(V,E) is a [1,2]dominating set if each v...
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On the complexity of the outerconnected bondage and the outerconnected reinforcement problems
Let G=(V,E) be a graph. A subset S ⊆ V is a dominating set of G if every...
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Total Domination in Unit Disk Graphs
Let G=(V,E) be an undirected graph. We call D_t ⊆ V as a total dominatin...
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A local characterization for perfect plane neartriangulations
We derive a local criterion for a plane neartriangulated graph to be pe...
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Algorithm and hardness results on neighborhood total domination in graphs
A set D⊆ V of a graph G=(V,E) is called a neighborhood total dominating ...
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An Efficient Matheuristic for the MinimumWeight Dominating Set Problem
A minimum dominating set in a graph is a minimum set of vertices such th...
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The polytope of legal sequences
A sequence of vertices in a graph is called a (total) legal dominating s...
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Total domination in plane triangulations
A total dominating set of a graph G=(V,E) is a subset D of V such that every vertex in V is adjacent to at least one vertex in D. The total domination number of G, denoted by γ _t (G), is the minimum cardinality of a total dominating set of G. A neartriangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that γ _t (G) ≤⌊2n/5⌋ for any neartriangulation G of order n≥ 5, with two exceptions.
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