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Connected domination in a signed graph and its complement.

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    • 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 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. [ABSTRACT FROM AUTHOR]
    • Abstract:
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