The common minimal common neighborhood dominating signed graphs

Abstract

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

Keywords

• Signed graphs
• Balance
• Switching
• Common minimal $CN$-dominating signed graph
• Negation