Domination hypergraphs of certain digraphs

Abstract

If $D=(V,A)$ is a digraph, its domination hypergraph $\mathcal{DH}(D) = (V,\mathcal{E})$ has the vertex set $V$ and $e \subseteq V$ is an edge of $\mathcal{DH}(D)$ if and only if e is a minimal dominating set of $D$. We investigate domination hypergraphs of special classes of digraphs, namely tournaments, paths and cycles. Finally, using a special decomposition/composition method we construct edge sets of domination hypergraphs of certain digraphs.