Bounds on the hop domination number of a tree.

A hop dominating set of a graph G is a set D of vertices of G if for every vertex of V (G) \ D, there exists u ∈ D such that d(u, v) = 2. The hop domination number of a graph G, denoted by γ_h(G), is the minimum cardinality of a hop dominating set of G. We prove that for every tree T of order n with l leaves and s support vertices we have (n − l − s + 4)/3 ≤ γ_h(G) ≤ n/2, and characterize the trees attaining each of the bounds. [ABSTRACT FROM AUTHOR]