Abstract
This paper considers the feedback number f (d, n) of Kautz digraph K (d, n), which is the minimum number of vertices in K (d, n) whose removal results in an acyclic digraph. Xu et al. have determined the exact values of f (d, n) for 1 ≤ n ≤ 7 and obtained an asymptotic formula f (d, n)=dn/n + dn -- 1/n-1 + O (ndn -- 4) for n ≥ 8. In this paper, we construct a feedbackvertex set of K (d, n) and obtain f (d, n)= dn/n +dn-1/n-1 + O (dn/2) for n ≥ 8 asymptotically.