(d, w)-控制数是一个度量共享网络资源的可靠性的重要参数。(1, 1)-控制数就是图论中的经典控制数, (d, w)-控制数是(1, 1)-控制数的一个直接推广。本文给出了计算(1, w)-控制数的一个下界方法和一个上界方法。应用这两个方法, 求出了超立方体的(1, n-1)-控制数和(1, n)-控制数, 求出了4基n立方体的(1, 2n - 1) -控制数和(1, 2n)-控制数, 求出了n维折叠超立方体的(1, n)-控制数。

(d, w) -dominating number is an important measuring parameter for the reliability of sharing common source in a network. (1, 1) -dominating number is also known as dominating number which is a classical parameter in graph theory. (d, w) -dominating number is a simple generalization of (1, 1) -dominating number. In this paper we present a lower bound and an upper bound for the calculating of (1, w) -dominating number. Using these two bounds, we find the (1, n - 1)-dominating number and (1, n)-dominating number for hypercube, we find the (1, 2n - 1) -dominating number and (1, 2n)-dominating number for 4-ary n-cube, and the (1, n)-dominating number for n dimensional folded hypercube.