Summary: Let \(R\) be a commutative ring with identity, \(Z(R)\) its set of zero-divisors, and \(H\) a nonempty proper multiplicative prime subset of \(R\). The generalized total graph of \(R\) is the simple undirected graph \(GT_{H}(R)\) with the vertex set \(R\) and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(x + y \in H\). In this paper, we investigate several graph theoretical properties of the complement \(\overline{GT_{H}(R)}\). In particular, we obtain a characterization for \(\overline{GT_{P}(R)}\) to be claw-free or unicyclic or pancyclic. Also, we obtain the clique number and chromatic number of \(\overline{GT_P(R)}\) and discuss the perfect, planar and outer planarity nature for \(\overline{GT_{P}(R)}\). Further, we discuss various domination parameters for \(\overline{GT_{P}(R)}\) where \(P\) is a prime ideal of \(R\).