A dominating set of a graph G is a subset D ⊆ V_{G} such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γ_{a}(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of V_{G} \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γ_{a}(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.
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