Warp: an integrated solution of high-speed parallel computing
Proceedings of the 1988 ACM/IEEE conference on Supercomputing
The J-machine multicomputer: an architectural evaluation
ISCA '93 Proceedings of the 20th annual international symposium on computer architecture
Fault Diameter of k-ary n-cube Networks
IEEE Transactions on Parallel and Distributed Systems
Performance of the CRAY T3E multiprocessor
SC '97 Proceedings of the 1997 ACM/IEEE conference on Supercomputing
Lee Distance and Topological Properties of k-ary n-cubes
IEEE Transactions on Computers
Linear array and ring embeddings in conditional faulty hypercubes
Theoretical Computer Science
Graph Theory With Applications
Graph Theory With Applications
Hamiltonian-like Properties of k-Ary n-Cubes
PDCAT '05 Proceedings of the Sixth International Conference on Parallel and Distributed Computing Applications and Technologies
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
Cycles embedding in hypercubes with node failures
Information Processing Letters
Node-disjoint paths in hierarchical hypercube networks
Information Sciences: an International Journal
On the spanning connectivity and spanning laceability of hypercube-like networks
Theoretical Computer Science
Note: Perfect matchings extend to Hamilton cycles in hypercubes
Journal of Combinatorial Theory Series B
Panconnectivity and edge-pancyclicity of 3-ary N-cubes
The Journal of Supercomputing
Guaranteed on-demand discovery of node-disjoint paths in ad hoc networks
Computer Communications
On Path Cover Problems in Digraphs and Applications to Program Testing
IEEE Transactions on Software Engineering
Embedding Long Paths in k-Ary n-Cubes with Faulty Nodes and Links
IEEE Transactions on Parallel and Distributed Systems
An effective algorithm for obtaining the minimal cost pair of disjoint paths with dual arc costs
Computers and Operations Research
Bipanconnectivity and Bipancyclicity in k-ary n-cubes
IEEE Transactions on Parallel and Distributed Systems
Many-to-Many Disjoint Path Covers in the Presence of Faulty Elements
IEEE Transactions on Computers
Strongly Hamiltonian laceability of the even k-ary n-cube
Computers and Electrical Engineering
Unpaired many-to-many vertex-disjoint path covers of a class of bipartite graphs
Information Processing Letters
Fault-free Hamiltonian cycles passing through a linear forest in ternary n-cubes with faulty edges
Theoretical Computer Science
| Hi-index | 5.23 |
The k-ary n-cube, Q"n^k, is one of the most popular interconnection networks. Let n=2 and k=3. It is known that Q"n^k is a nonbipartite (resp. bipartite) graph when k is odd (resp. even). In this paper, we prove that there exist r vertex disjoint paths {P"i|0@?i@?r-1} between any two distinct vertices u and v of Q"n^k when k is odd, and there exist r vertex disjoint paths {R"i|0@?i@?r-1} between any pair of vertices w and b from different partite sets of Q"n^k when k is even, such that @?"i"="0^r^-^1P"i or @?"i"="0^r^-^1R"i covers all vertices of Q"n^k for 1@?r@?2n. In other words, we construct the one-to-one r-disjoint path cover of Q"n^k for any r with 1@?r@?2n. The result is optimal since any vertex in Q"n^k has exactly 2n neighbors.