中文摘要：

网络的可靠性研究也称网络的容错性研究，一般分为容错性分析和容错性设计两个方面，有时容错性设计也称网络的容错性综合．容错性研究指的是假设网络的站点和连线以独立且相等概率失效情形下的可靠性分析．即计算一个已知网络因站点或站点之间的连线出现故障而引起整个网络失效的概率，或者在点边出现故障概率已知的情况下设计一个网络使其出现故障的概率最小．对于具有”个站点e条连线的所有不同拓扑结构的连通无向网络拓扑所组成的簇Ω（n，e）叫做网络簇，也叫簇网络．一般认为在每个网络簇中肯定存在一个网络，它的容错性要比该网络簇中其它网络的容错性好．事实上有些网络簇中不存在一致最优可靠性网络，但可以在这样的网络簇中找几个这样的网络，使得该网络簇中其它网络的容错性要比这几个网络中的某一个小．由这几个网络的容错性来衡量整个网络簇的容错性，而这几个被选定的网络所组成的集称之为这个网络簇的可靠性控制集．文中给出了当n≥8且为奇整数时，构建一类新网络簇Ω（n,n（n-1）/2-（n＋5）/5）的可靠性控制集．

英文摘要：

The research of network reliability is also called the research of fault-tolerant network which includes two aspects： reliability analysis and reliability design. Sometimes the reliability design of a network is called reliability synthesize. The main aim of reliability analysis is to com- pute the failure probability of networks. While, constructing a network with a minimum failure probability is the main aim of reliability design. In many applications, the topological structure of a network can be modeled as a undirected graph G with the same interconnection as the network. In this paper, we mainly investigate the reliability problem of a network with edge failure. Let Ω（n,e） be a family of networks which are constituted by all connected undirected networks with n vertices and e edges, then the notation Ω（n,e） is called the family of networks. Generally speak- ing, there must exist a network which has a better reliability than any other in this family of net- works. In fact there is no uniformly optimal reliable network in some families of networks, but there exist some networks which are more reliable than others in this family of networks. Then these certain networks can be used to evaluate the reliability of the whole family of networks, andthe set of such these networks are called reliability dominating set of the family of networks. This paper characterize a reliability dominating set of a new family of networks Ω（n,n（n-1）/2-（n＋5）/5）.where n is positive odd and n≥8.