Let G be a connected graph of minimum degree at least two. A set \(D\subseteq V(G)\) is a double total dominating set of G if \(|N_G(v)\cap D|\ge 2\) for every vertex \(v\in V(G)\) , where \(N_G(v)\) represents the open neighborhood of v. The double total domination number of G is the minimum cardinality among all double total dominating sets of G. In this article we study this parameter in some well-known graph operators defined from a connected graph G. In particular, we obtain the exact value for the double total domination number of the graph operator \(\texttt{R}(G)\) and the central graph \(\texttt{C}(G)\) . In addition, we obtain closed formulas for the double total domination number of the middle graph \(\texttt{M}(G)\) , the subdivision graph \(\texttt{S}(G)\) and the Mycielskian graph \(\mu (G)\) .
