An upper bound on the 2-outer-independent domination number of a tree Borne supérieure sur le nombre de 2-domination extérieurement-indépendante d’un arbre
نویسنده
چکیده
A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V (G)\D has a at least two neighbors in D, and the set V (G) \D is independent. The 2-outer-independent domination number of a graph G, denoted by γ 2 (G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have γ 2 (T ) ≤ (n + l)/2, and we characterize the trees attaining this upper bound.
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