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
Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes
Information Processing Letters
Fault-tolerant cycle embedding in dual-cube with node faults
International Journal of High Performance Computing and Networking
An Efficient Parallel Sorting Algorithm on Metacube Multiprocessors
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Cycles embedding in exchanged hypercubes
Information Processing Letters
Hamiltonian connectivity and globally 3*-connectivity of dual-cube extensive networks
Computers and Electrical Engineering
Mutually independent Hamiltonian cycles in dual-cubes
The Journal of Supercomputing
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A dual-cube uses low-dimensional hypercubes as basic components such that keeps the main desired properties of the hypercube. Each hypercube component is referred as a cluster. A (n+1)-connected dual-cube DC(n) has 2^2^n^+^1 nodes and the number of nodes in a cluster is 2^n. There are two classes with each class consisting of 2^n clusters. Each node is incident with exactly n+1 links where n is the degree of a cluster, one more link is used for connecting to a node in another cluster. In this paper, we show that every node of DC(n) lies on a cycle of every even length from 4 to 2^2^n^+^1 inclusive for n=3, that is, DC(n) is node-bipancyclic for n=3. Furthermore, we show that DC(n), n=3, is bipancyclic even if it has up to n-1 edge faults. The result is optimal with respect to the number of edge faults tolerant.