Bounding the Domination Number of a Tree in Terms of Its Annihilation Number

A set S of vertices in a graph G is a dominating set if every vertex of V − S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we show that for any tree T of order n ≥ 2, γ(T ) ≤ 3a(T )+2 4 , and we characterize the trees achieving this bound.