Critical concepts of restrained domination in signed graphs.

A signed graph Σ is a simple undirected graph in which each edge is either positive or negative. Restrained dominating set D in Σ is a restrained dominating set of the underlying graph | Σ | where the subgraph induced by the edges across Σ [ D : V ∖ D ] and within V ∖ D is balanced. The minimum cardinality of a restrained dominating set of Σ is called the restrained domination number, denoted by γ r (Σ). In this paper, we initiate the study on various critical concepts to investigate the effect of edge removal or edge addition on restrained domination number in signed graphs. [ABSTRACT FROM AUTHOR]