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An upper bound on the total outer-independent domination number of a tree

Krzywkowski M.

Opuscula Mathematica

2012

Vol. 32, no. 1

153-158

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 [formula], 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 [formula], and we characterize the trees attaining this upper bound.