ICPADS '06 Proceedings of the 12th International Conference on Parallel and Distributed Systems - Volume 1
Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes
Parallel Computing
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
Fault-tolerant pancyclicity of augmented cubes
Information Processing Letters
Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Sciences: an International Journal
Fault-free Hamiltonian cycles in crossed cubes with conditional link faults
Information Sciences: an International Journal
Conditional fault Hamiltonicity of the complete graph
Information Processing Letters
Fault-free Hamiltonian cycles in twisted cubes with conditional link faults
Theoretical Computer Science
Edge-fault-tolerant Hamiltonicity of pancake graphs under the conditional fault model
Theoretical Computer Science
Embedding a family of 2D meshes into Möbius cubes
WSEAS Transactions on Mathematics
Embedding Hamiltonian cycles in alternating group graphs under conditional fault model
Information Sciences: an International Journal
Fault-free longest paths in star networks with conditional link faults
Theoretical Computer Science
Embedding fault-free cycles in crossed cubes with conditional link faults
The Journal of Supercomputing
Path embeddings in faulty 3-ary n-cubes
Information Sciences: an International Journal
Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links
Information Sciences: an International Journal
Matching preclusion for k-ary n-cubes
Discrete Applied Mathematics
Information Sciences: an International Journal
A family of Hamiltonian and Hamiltonian connected graphs with fault tolerance
The Journal of Supercomputing
Conditional edge-fault-tolerant Hamiltonicity of dual-cubes
Information Sciences: an International Journal
Panconnectivity and edge-pancyclicity of k-ary n-cubes with faulty elements
Discrete Applied Mathematics
Pancyclicity of ternary n-cube networks under the conditional fault model
Information Processing Letters
Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model
SIAM Journal on Discrete Mathematics
Hamiltonian paths and cycles with prescribed edges in the 3-ary n-cube
Information Sciences: an International Journal
Hamiltonian cycles passing through linear forests in k-ary n-cubes
Discrete Applied Mathematics
Hamiltonian cycles through prescribed edges in k-ary n-cubes
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
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
Conditional Diagnosability of k-Ary n-Cubes under the PMC Model
ACM Transactions on Design Automation of Electronic Systems (TODAES)
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
| Hi-index | 0.01 |
We consider the fault-tolerant capabilities of networks of processors whose underlying topology is that of the k-ary n-cube $Q_n^k$, where $k\geq 3$ and $n\geq 2$. In particular, given a copy of $Q_n^k$ where some of the interprocessor links may be faulty but where every processor is incident with at least two healthy links, we show that if the number of faults is at most 4n-5, then $Q_n^k$ still contains a Hamiltonian circuit, but that there are situations where the number of faults is 4n-4 (and every processor is incident with at least two healthy links) and no Hamiltonian circuit exists. We also remark that given a faulty $Q_n^k$, the problem of deciding whether there exists a Hamiltonian circuit is NP-complete.