An Upper Bound on the Total Outer-independent Domination Number of a Tree
نویسنده
چکیده
A total outer-independent dominating set of a graph G = (V (G), E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \D is independent. The total outer-independent domination number of a graph G, denoted by γ t (G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n ≥ 4, with l leaves and s support vertices we have γ t (T ) ≤ (2n+ s− l)/3, and we characterize the trees attaining this upper bound.
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