Connected domination in a signed graph and its complement

Abstract

A signed graph Σ = (G, σ) is a graph with a sign attached to each arc. A subset S of V (Σ) is called a dominating set of Σ if |N+ (v)  ∩ S| > |N- (v)  ∩ S| for all v ∈ V - S . A dominating set S ⊆ V is a connected dominating set of Σ if <S> is connected. The minimum cardinality of a connected dominating set of Σ denoted by γsc, is called the connected domination number of Σ . In this paper, we introduce the connected domination number in a signed graph Σ and study different bounds and characterization of the connected domination number in a signed graph Σ . Furthermore, we find the best possible upper and lower bounds for γ sc ( Σ ) + γ sc ( Σ α c ) where Σ is connected.