  In this paper, we present a detailed study of the reach distance-layer
structure of the De Bruijn and Kautz digraphs, and we apply our analysis to the
performance evaluation of deflection routing in De Bruijn and Kautz networks.
Concerning the distance-layer structure, we provide explicit polynomial
expressions, in terms of the degree of the digraph, for the cardinalities of
some relevant sets of this structure. Regarding the application to defection
routing, and as a consequence of our polynomial description of the
distance-layer structure, we formulate explicit rational expressions, in terms
of the degree of the digraph, for some probabilities of interest in the
analysis of this type of routing.
  De Bruijn and Kautz digraphs are fundamental examples of digraphs on alphabet
and iterated line digraphs. If the topology of the network under consideration
corresponds to a digraph of this type, we can perform, in principle, a similar
vertex layer description.
