The twin domination number in generalized de Bruijn digraphs

Let G=(V,A) be a digraph. A set T of vertices of G is a twin dominating set of G if for every vertex v∈V∖T, there exist u,w∈T (possibly u=w) such that arcs (u,v),(v,w)∈A. The twin domination number γ∗(G) of G is the cardinality of a minimum twin dominating set of G. In this paper we investigate the twin domination number in generalized de Bruijn digraphs GB(n,d). For the digraphs GB(n,d), we first establish sharp bounds on the twin domination number. Secondly, we give the exact values of the twin domination number for several types of GB(n,d) by constructing minimum twin dominating sets in the digraphs. Finally, we present sharp upper bounds for some special generalized de Bruijn digraphs.