The common minimal common neighborhood dominating signed graphs

In this paper, we define the common minimal common neighborhood dominating signed graph (or common minimal $CN$-dominating signed graph) of a given signed graph and offer a structural characterization of common minimal $CN$-dominating signed graphs. In the sequel, we also obtained switching equivalence characterization: $overline{Sigma} sim CMCN(Sigma)$, where $overline{Sigma}$ and $CMCN(Sigma)$ are complementary signed graph and common minimal $CN$-signed graph of $Sigma$ respectively.