中文摘要：

对于任意的正整数l，强连通图G的顶点子集D被称为距离l-控制集。是指对于任意顶点V不属于D，D中至少含有一个顶点u，使得距离dG（u，v）≤l．图G距离l-控制数re（G）是指G中所有距离l-控制集的基数的最小者．本文给出了广义de Bruijn和广义Kautz有向图的距离l-控制数的上界和下界。并且给出当它们的距离2-控制数达到下界时的一个充分条件．从而得到对于de Bruijn有向图B（d，k）的距离2-控制数r2（B（d，k））=[d^k/（d^2＋d＋1）]．在该文结尾，我们猜想Kautz有向图K（d，k）的距离2-控制数r2（K（d，k））=[（d^k＋d^k-1）/（d^2＋d＋1）]．

英文摘要：

The distance l-domination number rl（G） of a strongly connected digraph G is the minimum number r for which there is a set D 包含 V（G） with cardinality r such that any vertex v 不属于 D can be reached within distance l from some vertex in D. In this paper, we establish a lower bound and an upper bound for rl of a generalized de Bruijn digraph and a generalized Kautz digraph, and also give a sufficient condition for these digraphs whose r2 are equal to the lower bounds. As a consequence, for the de Bruijn digraph B（d, k）, we determine that r2（B（d, k）） = [d^k/（d^2＋d＋1）] . At the end of this paper, we conjecture r2（K（d,k））=[（d^k＋d^k-1）/（d^2＋d＋1）]