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A paired-dominating set of a graph G=(V, E) with no isolated vertex is a  dominating set of vertices whose induced subgraph has a perfect matching. The  paired-domination number of G, denoted by γpr(G), is the minimum cardinality  of a paired-dominating set of 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 prove  that for any tree T of order n≥2,γpr(T)≤ 4a(T)+2/3 and we characterize the  trees achieving this bound.

Bounding the paired-domination number of a tree in terms of its annihilation number