Embedding of rings in 2-D meshes and tori with faulty nodes
Journal of Systems Architecture: the EUROMICRO Journal
Fault-Tolerant Embeddings of Hamiltonian Circuits in k-ary n-Cubes
SIAM Journal on Discrete Mathematics
Linear array and ring embeddings in conditional faulty hypercubes
Theoretical Computer Science
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Sciences: an International Journal
Edge-bipancyclicity of conditional faulty hypercubes
Information Processing Letters
Embedding Long Paths in k-Ary n-Cubes with Faulty Nodes and Links
IEEE Transactions on Parallel and Distributed Systems
Bipanconnectivity and Bipancyclicity in k-ary n-cubes
IEEE Transactions on Parallel and Distributed Systems
Graph Theory
Hamiltonian properties of honeycomb meshes
Information Sciences: an International Journal
Fault-free Hamiltonian cycles passing through a linear forest in ternary n-cubes with faulty edges
Theoretical Computer Science
Hamiltonian path embeddings in conditional faulty k-ary n-cubes
Information Sciences: an International Journal
| Hi-index | 5.23 |
It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. In this paper, we consider the faulty k-ary n-cube with even k=4 and n=2 such that each vertex of the k-ary n-cube is incident with at least two healthy edges. Based on this requirement, we prove that the k-ary n-cube contains a hamiltonian path joining every pair of vertices which are in different parts, even if it has up to 4n-6 edge faults.