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.

Keywords

• hypergraph
• dominating set
• directed graph