Reliability evaluation of conditional recursive networks under h-conditional restriction

Abstract

As the number of links and processors in an interconnection network increases, faulty links and processors are constantly emerging. When a network fails, how to evaluate the state of the network and optimize the reliability of the network itself is the focus of attention in recent years. Therefore, the design of network structure and network reliability evaluation are particularly significant. In recent years, connectivity, especially h-conditional restricted connectivity, has been widely discussed by scholars. In this paper, a family of composite network is constructed on the basis of complete graph $K_l$ ($l\ge 3$ is an odd integer), named conditional recursive networks (simply called CRNs). It contains the common network alternating group network ($A{N}_m$) and some unknown networks. In order to further reflect the reliability of composite network CRNs, we determine connectivity and h-conditional restricted connectivity for $0\le h\le l-1$. As an application, we get the connectivity and h-conditional restricted connectivity of $A{N}_m$ directly.