Fault tolerant hypercube networks with minimal redundancy

The popularity of hypercube networks motivated several researchers to propose and study fault-tolerant hypercube-based networks. We establish the lower bound on hardware redundancy that is necessary to tolerate a single node or link failure. We introduce a hypercube-based network with one extra node and four extra links and prove that the network is one node (link) Hamiltonian. We also prove that no less than four extra links can be employed to tolerate any single failure. The proposed network which is attractive for small size networks can be utilized as the building block of large size, highly efficient, hypercube networks capable of tolerating multiple faults.<>