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The domination number of a graph \( G \), \( \gamma(G) \), and the domination graph of a digraph \( D \), \( dom(D) \), are integrated in this paper. The \( \gamma \)-set di domination graph of the complete biorientation of a graph \( G \), \( dom_{\gamma}(\overset{\leftrightarrow}{G}) \), is created. All \( \gamma \)-sets of specific trees \( T \) are found, and \( dom_{\gamma}(\overset{\leftrightarrow}{T}) \) is characterized for those classes.