Generalized Kautz digraph

Generalized Kautz digraph --- обобщенный орграф Каутца.

The generalized Kautz digraph [math]\displaystyle{ G_{K}(n,d) }[/math] is defined by the following congruence equations:

[math]\displaystyle{ \left\{\begin{array}{l} V(G_{K}(n,d)) = \{0,1,2, \ldots, n-1\}, \\ A(G_{K}(n,d)) = \{(x,y)|\, y \equiv -dx - i\pmod{n}, 0 \lt i \leq d\} \end{array}\right. }[/math]

If [math]\displaystyle{ n = d(d-1)^{D-1} }[/math], [math]\displaystyle{ G_{K}(n,d) }[/math] is the Kautz digraph [math]\displaystyle{ K(d-1,D) }[/math].