Topological Properties of Hypercubes
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
A transputer-based reconfigurable parallel system
NATUG-6 Proceedings of the sixth conference of the North American Transputer Users Group on Transputer research and applications 6
The REFINE multiprocessor—theoretical properties and algorithms
Parallel Computing
Parallel Edge-Region-Based Segmentation Algorithm Targeted at Reconfigurable MultiRing Network
The Journal of Supercomputing
Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes
Information Processing Letters
Fault-Tolerant Routing and Disjoint Paths in Dual-Cube: A New Interconnection Network
ICPADS '01 Proceedings of the Eighth International Conference on Parallel and Distributed Systems
Efficient Collective Communications in Dual-Cube
The Journal of Supercomputing
Linear array and ring embeddings in conditional faulty hypercubes
Theoretical Computer Science
The super laceability of the hypercubes
Information Processing Letters
Graph Theory With Applications
Graph Theory With Applications
Path bipancyclicity of hypercubes
Information Processing Letters
Cycles embedding in hypercubes with node failures
Information Processing Letters
Note: Perfect matchings extend to Hamilton cycles in hypercubes
Journal of Combinatorial Theory Series B
Fault-tolerant cycle embedding in dual-cube with node faults
International Journal of High Performance Computing and Networking
The edge-pancyclicity of dual-cube extensive networks
CEA'08 Proceedings of the 2nd WSEAS International Conference on Computer Engineering and Applications
On embedding cycles into faulty dual-cubes
Information Processing Letters
Theory of Computing Systems - Special Issue: Symposium on Parallelism in Algorithms and Architectures 2006; Guest Editors: Robert Kleinberg and Christian Scheideler
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
Binomial-tree fault tolerant routing in dual-cubes with large number of faulty nodes
CIS'04 Proceedings of the First international conference on Computational and Information Science
Mutually independent Hamiltonian cycles in k-ary n-cubes when k is even
Computers and Electrical Engineering
On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube
Journal of Combinatorial Optimization
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The hypercube family Q n is one of the most well-known interconnection networks in parallel computers. With Q n , dual-cube networks, denoted by DC n , was introduced and shown to be a (n+1)-regular, vertex symmetric graph with some fault-tolerant Hamiltonian properties. In addition, DC n 's are shown to be superior to Q n 's in many aspects. In this article, we will prove that the n-dimensional dual-cube DC n contains n+1 mutually independent Hamiltonian cycles for n驴2. More specifically, let v i 驴V(DC n ) for 0驴i驴|V(DC n )|驴1 and let $\langle v_{0},v_{1},\ldots ,v_{|V(\mathit{DC}_{n})|-1},v_{0}\rangle$ be a Hamiltonian cycle of DC n . We prove that DC n contains n+1 Hamiltonian cycles of the form $\langle v_{0},v_{1}^{k},\ldots,v_{|V(\mathit{DC}_{n})|-1}^{k},v_{0}\rangle$ for 0驴k驴n, in which v i k 驴v i k驴 whenever k驴k驴. The result is optimal since each vertex of DC n has only n+1 neighbors.