The common minimal dominating signed graph

In this paper, we define the common minimal dominating signedgraph of a given signed graph and offer a structuralcharacterization of common minimal dominating signed graphs. Inthe sequel, we also obtained switching equivalencecharacterizations: $overline{S} sim CMD(S)$ and $CMD(S) simN(S)$, where $overline{S}$, $CMD(S)$ and $N(S)$ are complementarysigned graph, common minimal signed graph and neighborhood signedgraph of $S$ respectively.