Let F v be a set of faulty nodes in an n-dimensional hypercube, denoted by Q n. Also, let F e be a set of faulty edges in which at least one end-node of each edge is faulty. An edge in Q n is said to be critical if it is either fault-free or in F e. In this paper, we prove that, for up to 2n-4 faulty nodes and/or edges, an n-dimensional hypercube contains a fault-free cycle of every even length from 4 to 2 n-2|F v| in which each node is incident to at least two critical edges. Our result improves on the previously best known results reported in the literature.
All Science Journal Classification (ASJC) codes
- Electrical and Electronic Engineering