A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
System design of the J-Machine
AUSCRYPT '90 Proceedings of the sixth MIT conference on Advanced research in VLSI
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Embeddings of Hamiltonian Circuits in k-ary n-Cubes
SIAM Journal on Discrete Mathematics
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
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
Strongly Hamiltonian laceability of the even k-ary n-cube
Computers and Electrical Engineering
Path embeddings in faulty 3-ary n-cubes
Information Sciences: an International Journal
Blue Gene/L torus interconnection network
IBM Journal of Research and Development
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
Embedding hamiltonian paths in k-ary n-cubes with conditional edge faults
Theoretical Computer Science
Pancyclicity of k-ary n-cube networks with faulty vertices and edges
Discrete Applied Mathematics
Paired many-to-many disjoint path covers of the hypercubes
Information Sciences: an International Journal
Fault-tolerant embedding of cycles of various lengths in k-ary n-cubes
Information and Computation
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The class of k-ary n-cubes represents the most commonly used interconnection topology 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-5 edge faults and this result is optimal.