无向超环面网$C(3,3,\ldots,3)$的$(n,2n)$控制数

$(n,2n)$-Dominating Numbers of Undirected Toroidal Mesh $C(3,3,\ldots, 3)$

中文关键词:  可靠性  宽直径  无向超环面网  $(d,k)$控制数.

英文关键词:reliability  wide-diameter  undirected toroidal mesh  $(d,k)$-dominating number.

中文摘要:

      $(d,k)$控制数是用来刻画容错网络中资源共享可靠性的一个新参数. 本文证明：$n\, (n\geq 3)$维无向超环面网$C(3,3,\ldots,3)$的$(n,2n)$控制数为 $3$.

英文摘要:

      The $(d,k)$-dominating number is a new measure to characterize reliability of resource-sharing in fault tolerant networks. This paper obtains that the $(n,2n)$-dominating number of the $n$-dimensional undirected toroidal mesh $C(3,3,\ldots,3)$ is equal to $3$ ($n\geq 3$).