Reliability evaluation for bijection-connected networks based on the super Pk-connectivity

With the need for large-scale networks evolving in a variety of fields, such as cloud/edge computing, social networks, privacy protection, etc., the network's robustness against faulty clusters has recently gained more attention. The family of bijection-connected networks includes numerous instances of remarkable network topologies, for example, hypercubes, Möbius cubes, crossed cubes, etc. For a network whose underlying topology is modeled by a graph G, its node-connectivity, κ(G), is a key performance index of network robustness, which is formalized as the total number of nodes in the smallest node-cut of G. Apparently, κ(G) happens to be bounded above by G's minimum degree. A node-cut is trivial if it is nothing but an arbitrary node's neighborhood. Then, G can be r-connected if 1≤r≤κ(G). To say the least, if each smallest node-cut of G is trivial, G is super connected. The super Pk-connectivity is an innovative assessment to quantify the connectedness level of G, where Pk notates a path consisting of k nodes (k≥1). This article aims to investigate the super Pk-connectivity for the bijection-connected networks. With regard to some specific instances, such as hypercubes, locally twisted cubes, etc., a sufficient and necessary condition is established to identify whether they are really super Pk-connected.