Two short proofs on total domination
نویسنده
چکیده
A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph γt (G) is the minimum size of a total dominating set. We provide a short proof of the result that γt (G) ≤ 2 3 n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.
منابع مشابه
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LetG = (V,E) be a finite, simple, undirected graph. A set S ⊆ V is called a total dominating set if every vertex of V is adjacent to some vertex of S. Interest in total domination began when the concept was introduced by Cockayne, Dawes, and Hedetniemi [6] in 1980. In 1998, two books on the subject appeared ([11] and [12]), followed by a survey of more recent results in 2009 [15]. The total dom...
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ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 33 شماره
صفحات -
تاریخ انتشار 2013