The common minimal dominating signed graph

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