Theo-Conjecture for connected cographs

Let $G$) be a connected cograph with no universal vertex. For the co-components $H_{(1)}$ and $H_{(2)}$ defined as in Proposition~, Theo-Conjecture.

$$\operatorname{zdmg}(G)=q(H_{(1)})+q(H_{(2)}).$$

The cograph condition is essential to the proposed extension: in a general join, internal common neighbors may allow a more efficient confinement strategy. Whether the asserted formula holds for all connected cographs remains open.