Constructing a reliability dominating set of a new family of networks

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 compute 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 speaking, there must exist a network which has a better reliability than any other in this family of networks. 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, and the 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 2), where n is positive odd and n ≥ 8.