A new digraphs composition with applications to de Bruijn and generalized de Bruijn digraphs

Abstract

In this paper, we introduce a new operation on digraphs that we apply to different cases; we give new results about de Bruijn digraphs and generalized de Bruijn digraphs. We prove that this new operation commutes with the operation of taking the line digraph. In particular, we give a simple construction of the Kautz digraph of diameter n from two de Bruijn digraphs of diameter n − 1 and n. We also study k-factors in the composed digraph with application to the counting of 1-factors of de Bruijn and Kautz digraphs.