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A signed graph (digraph) \( \Sigma \) is an ordered triple \( (V, E, \sigma) \) (respectively, \( (V, \mathcal{A}, \sigma) \)), where \( |\Sigma| := (V, E) \) (respectively, \( (V, \mathcal{A}) \)) is a graph (digraph), called the underlying graph (underlying digraph) of \( \Sigma \), and \( \sigma \) is a function that assigns to each edge (arc) of \( |\Sigma| \) a weight \( +1 \) or \( -1 \). Any edge (arc) \( e \) of \( \Sigma \) is said to be positive or negative according to whether \( \sigma(e) = +1 \) or \( \sigma(e) = -1 \). A subset \( D \subseteq V \) of vertices of \( \Sigma \) is an absorbent (respectively, a dominating set) of \( \Sigma \) if there exists a marking \( \mu: V \to \{+1, -1\} \) of \( \Sigma \) such that every vertex \( u \) of \( \Sigma \) is either in \( D \) or
\[
O(u) \cap D \neq \emptyset \quad \text{and} \quad \sigma(u, v) = \mu(u) \mu(v) \quad \forall \quad v \in O(u) \cap D,
\]
(respectively,
\[
I(u) \cap D \neq \emptyset \quad \text{and} \quad \sigma(u, v) = \mu(u) \mu(v) \quad \forall \quad v \in I(u) \cap D),
\]
where \( O(u) \) (\( I(u) \)) denotes the set of vertices \( v \) of \( \Sigma \) that are joined by the outgoing arcs \( (u, v) \) from \( u \) (incoming arcs \( (v, u) \) at \( u \)). Further, an absorbent (dominating set) of \( \Sigma \) that is independent is called a kernel (solution) of \( \Gamma \). The main aim of this paper is to initiate a study of absorbents and dominating sets in a signed graph (signed digraph), extending the existing studies on these special sets of vertices in a graph (digraph).