Connected -tuple twin domination in de Bruijn and Kautz digraphs

For a digraph G , a k -tuple twin dominating set D of G for some fixed k ≥ 1 is a set of vertices such that every vertex is adjacent to at least k vertices in D , and also every vertex is adjacent from at least k vertices in D . If the subgraph of G induced by D is strongly connected, then D is called a connected k-tuple twin dominating set of G . In this paper, we give constructions of minimal connected k -tuple twin dominating sets for de Bruijn digraphs and Kautz digraphs.