Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links
Information Sciences: an International Journal
Analytical modelling of networks in multicomputer systems under bursty and batch arrival traffic
The Journal of Supercomputing
Panconnectivity and edge-pancyclicity of k-ary n-cubes with faulty elements
Discrete Applied Mathematics
Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges
Information Sciences: an International Journal
One-to-one disjoint path covers on k-ary n-cubes
Theoretical Computer Science
Embedding hamiltonian paths in k-ary n-cubes with conditional edge faults
Theoretical Computer Science
Fault tolerance in k-ary n-cube networks
Theoretical Computer Science
Fault-tolerant embedding of cycles of various lengths in k-ary n-cubes
Information and Computation
Hamiltonian path embeddings in conditional faulty k-ary n-cubes
Information Sciences: an International Journal
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Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Qkn in which the number of node faults fv and the number of link faults fe are such that fn+fe ≤ 2n-2. We prove that given any two healthy nodes s and e of Qkn, there is a path from s to e of length at least kn-2fn-1 (resp. kn-2fn-2) if the nodes s and e have different (resp. the same) parities (the parity of a node in Qkn is the sum modulo 2 of the elements in the n-tuple over {0,1,...,k-1} representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n=2.