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For each vertex \( v \) in a graph \( G \), let there be associated a particular type of a subgraph \( F_v \) of \( G \). In this context, the vertex \( v \) is said to dominate \( F_v \). A set \( S \) of vertices of \( G \) is called a full dominating set if every vertex of \( G \) belongs to a subgraph \( F_v \) of \( G \) for some \( v \in S \) and every edge of \( G \) belongs to a subgraph \( F_w \) of \( G \) for some \( w \in S \). The minimum cardinality of a full dominating set of \( G \) is its full domination number \( \gamma_F(G) \). A full dominating set of \( G \) of cardinality \( \gamma_F(G) \) is called a \( \gamma_F \)-set of \( G \).
We study three types of full domination in graphs: full star domination, where \( F_v \) is the maximum star centered at \( v \); full closed domination, where \( F_v \) is the subgraph induced by the closed neighborhood of \( v \); and full open domination, where \( F_v \) is the subgraph induced by the open neighborhood of \( v \).
A subset \( T \) of a \( \gamma_F \)-set \( S \) in a graph \( G \) is a forcing subset for \( S \) if \( S \) is the unique \( \gamma_F \)-set containing \( T \). The forcing full domination number of \( S \) in \( G \) is the minimum cardinality of a forcing subset for \( S \), and the forcing full domination number \( f_{\gamma_F}(G) \) of the graph \( G \) is the minimum forcing full domination number among all \( \gamma_F \)-sets of \( G \).
We present several realization results concerning forcing parameters in full domination.