The common minimal common neighborhood dominating signed graphs

Abstract

‎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.