Let \((R,\mathfrak {m})\) be a local ring and C be an R-complex in \(\text {D}_{\Box }^f(R)\) . Then, we prove that C is a dualizing complex of R if and only if C is a Cohen-Macaulay semidualizing complex of type one or . Also, we show that a semidualizing complex C is dualizing if and only if there exists a type one Cohen-Macaulay R-module of finite \(G_{C}\) -dimension or there exists a type one Cohen-Macaulay R-complex of finite \(G_{C}\) -dimension such that \({\textsf{dim}}_R(X)={\textsf{dim}}_R(C)-{\textsf{grade}}_C(X)\) . Furthermore, for a semidualizing R-complex C, we prove that \(C\sim R\) if and only if there exists a type one Cohen-Macaulay R-module M which belongs to the Auslander class \(\mathcal {A}_C(R)\) .
