Abstract
The hypercube has been widely used as the interconnection network in parallel computers. The n-dimensional hypercube Q n is a graph having 2 n vertices each labeled with a distinct n-bit binary strings. Two vertices are linked by an edge if and only if their addresses differ exactly in the one bit position. Let f v denote the number of faulty vertices in Q n . For n ⩾ 3 , in this paper, we prove that every fault-free edge and fault-free vertex of Q n lies on a fault-free cycle of every even length from 4 to 2 n − 2 f v inclusive even if f v ⩽ n − 2 . Our results are optimal.
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