Twin domination in generalized Kautz 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 (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 consider the twin domination number in generalized Kautz digraphs
GK(n, d). In these digraphs, we establish bounds on the twin domination number and give a sufficient condition for the twin
domination number attaining the lower bound. We give the exact values of the twin domination numbers by constructing
minimum twin dominating sets for some special generalized Kautz digraphs.