De Bruijn and Kautz digraphs of a rooted tree

In this paper we define the De Bruijn digraphs B(D,m) and the Kautz digraphs K(D,m) of a digraph D in such a way that we recover the original definitions when the digraph D is a path. We establish some general properties of the De Bruijn digraph and the Kautz digraph of a digraph D. We also determine the structure of such digraphs when D is a rooted tree.