Abstract
In a graph G, a vertex dominates itself and its neighbors. A set S of vertices in a graph G is a double dominating set if S dominates every vertex of G at least twice. The double domination number γx2(G) is the minimum cardinality of a double 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, different from P4, γx2(T) ≤ 3a(T)+1. 2.
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