Vulnerability of the Hypercube Network Based on $$P_2$$-cuts

The abstract graph G can model an interconnection network’s topology. A cluster C in G is a node subset of G such that the subgraph induced by C is connected. Theoretically speaking, the order of the maximal component in G from which certain faulty clusters are removed can be referred as an index of fault tolerability. A path consisting of k distinct nodes is abbreviated as $$P_k$$ . A set F of clusters of G is a $$P_2$$ -cut if (i) all clusters of F induce subgraphs that are isomorphic to $$P_2$$ , and (ii) $$G-F$$ is trivial or disconnected. Because of the growing popularity of the hypercube architecture $$Q_n$$ in real-world supercomputers, this paper is devoted to exploring the vulnerability of $$Q_n$$ based on $$P_2$$ -cuts.