Abstract
Let k be a positive integer and G = (V, E) be a simple graph. A subset S ⊆ V is dominating in G, if for each vertex v ∊ V \\ S, N(v) ∩ S ≠ . In 1985, Fink and Jacobson gave a generalization of the concept of dominating sets in graphs. A subset S of V is k-dominating in G, if every vertex of V \\ S is adjacent to at least k vertices in S. In this paper, we characterize vertices that are in all or in no minimum k-dominating sets in a tree for k ≥ 2.
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