Connected kk-tuple twin domination in de Bruijn and Kautz digraphs

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