Let G(V(G), E(G)) be a nontrivial connected graph and let \(D\subseteq V(G)\) . The set D is a dominating set of G if every vertex in \(V(G)\setminus D\) has at least one neighbor in D. Further, if every vertex in D has either zero or at least two neighbors in \(V(G)\setminus D\) , then D is a certified dominating set of G. The (certified) domination number of G is the minimum cardinality among all (certified) dominating sets of G. In this article, a constructive characterization of trees with equal domination and certified domination numbers is presented.
