Extension of Non - faulty

In this study we considered and analyzed the diierent cases of node-and link-faults in a hypercube multiprocessor. We revealed that, the direct use of sharp product operation is not suucient to discard only computational part (processor and memory), when only this part of node is faulty. We also showed that in case when some links in communication part (router) incident to a healthy node are faulty, the sharp product operation does not allow to leave the healthy links and the node incident to these links in the set of healthy subcubes. In order to remove this deeciency, we propose formal procedures with aid of which we can subtract rst only the faulty node, excluding the healthy links incident to this node and second only the faulty links, excluding also the healthy nodes incident to these links. The procedures are independent from the number and scattering of faulty elements in hypercube. Thus, the proposed procedures allow to obtain a set of extended fault-free subcubes, that is a beginning set for further manipulation in hypercube multiprocessors and increase the reliability of such systems.