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Fault Free Hamiltonian Cycles Passing through Edges
The k -ary n -cube is one of the most attractive interconnectionnetworks for parallel and distributed systems. In this paper, we consider the problem of a fault-free hamiltonian cycle passing through prescribed edges in a k -ary n -cube with some faulty edges.
The following result is obtained: For any and , let , with , . Then there exists a hamiltonian cycle passing through all edges of in if and only if the subgraph induced by consists of pairwise vertex-disjoint paths. It improves the result given by Yang and Wang .
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