System design of the J-Machine
AUSCRYPT '90 Proceedings of the sixth MIT conference on Advanced research in VLSI
Embedding complete trees into the hypercube
Discrete Applied Mathematics
Fast Sorting Algorithms on a Linear Array with a Reconfigurable Pipelined Bus System
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Embeddings of Hamiltonian Circuits in k-ary n-Cubes
SIAM Journal on Discrete Mathematics
On Balancing Sorting on a Linear Array
IEEE Transactions on Parallel and Distributed Systems
Efficient embeddings of ternary trees into hypercubes
Journal of Parallel and Distributed Computing
Fault Hamiltonicity and Fault Hamiltonian Connectivity of the Arrangement Graphs
IEEE Transactions on Computers
Optimal Path Embedding in Crossed Cubes
IEEE Transactions on Parallel and Distributed Systems
Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks with Faulty Elements
IEEE Transactions on Parallel and Distributed Systems
Mapping Cycles and Trees on Wrap-Around Butterfly Graphs
SIAM Journal on Computing
Optimal fault-tolerant embedding of paths in twisted cubes
Journal of Parallel and Distributed Computing
Dense sets and embedding binary trees into hypercubes
Discrete Applied Mathematics
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements
Theoretical Computer Science
The bipanconnectivity and m-panconnectivity of the folded hypercube
Theoretical Computer Science
Panconnectivity and edge-pancyclicity of 3-ary N-cubes
The Journal of Supercomputing
Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m,4)
Theoretical Computer Science
Edge-bipancyclicity of a hypercube with faulty vertices and edges
Discrete Applied Mathematics
Embedding cycles and paths in a k-ary n-cube
ICPADS '07 Proceedings of the 13th International Conference on Parallel and Distributed Systems - Volume 01
Note: Embedding graphs as isometric medians
Discrete Applied Mathematics
Embedding Long Paths in k-Ary n-Cubes with Faulty Nodes and Links
IEEE Transactions on Parallel and Distributed Systems
Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links
Information Sciences: an International Journal
Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges
Information Sciences: an International Journal
Hamiltonian cycles passing through linear forests in k-ary n-cubes
Discrete Applied Mathematics
Pancyclicity of OTIS (swapped) networks based on properties of the factor graph
Information Processing Letters
Pancyclicity of k-ary n-cube networks with faulty vertices and edges
Discrete Applied Mathematics
Fault tolerance in k-ary n-cube networks
Theoretical Computer Science
Panconnectivity of n-dimensional torus networks with faulty vertices and edges
Discrete Applied Mathematics
Hamiltonian path embeddings in conditional faulty k-ary n-cubes
Information Sciences: an International Journal
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The class of k-ary n-cubes represents the most commonly used interconnection topology for parallel and distributed computing systems. In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for odd integer k with respect to the panconnectivity and pancyclicity. By studying first the fault panconnectivity of two-dimensional torus networks and then using an induction argument, we prove that in a k-ary n-cube Q"n^k with odd k=3, every pair of healthy vertices of Q"n^k are connected by fault-free paths of lengths from n(k-1)-1 to |V(Q"n^k-F)|-1 and every healthy edge is contained in fault-free cycles of lengths from n(k-1) to |V(Q"n^k-F)| for any set F of faulty elements (vertices and/or edges) with |F|@?2n-3. Finally, examples show that our results are best possible in some sense.