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Disjoint Paths in Folded Hypercubes with Deleting Some Edges

Dan Jin, Hongmei Liu


Let u be the smallest degree node in a hypercube network with some faulty edges. Suppose that the number of fault-free edges incident with u is not more than that of the others, and denote this number by k. In this article, we mainly concentrate on the conditional edge-fault-tolerant paths embedding of the n-dimensional hypercube and folded hypercube. In view of this purpose, we prove that there exist k disjoint paths between the smallest degree node and its neighbor which contain all nodes in an n-cube with at most n−2 faulty edges. Based on the result, it has been found that for the smallest degree node and its neighbor there are k internal-disjoint paths between them, which traverse all vertices of an n-dimensional folded cube with at most n − 1 faulty edges.


hypercube, folded hypercube, fault-tolerance, path.

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