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
Graph Theory With Applications
Graph Theory With Applications
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
Path bipancyclicity of hypercubes
Information Processing Letters
Cycles embedding in hypercubes with node failures
Information Processing Letters
Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements
Theoretical Computer Science
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
On the enhanced hyper-hamiltonian laceability of hypercubes
CEA'09 Proceedings of the 3rd WSEAS international conference on Computer engineering and applications
An Efficient Parallel Sorting Algorithm on Metacube Multiprocessors
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
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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The hypercube family Qn is one of the most well-known interconnection networks in parallel computers, e.g. see [3, 6]. Using Qn, Li et al. introduced dual-cube networks DC(n) and show the vertex symmetry and some fault-tolerant hamiltonian properties of DC(n) [7, 8]. By replacing Qn with any arbitrary graph G in DC(n), a new family of interconnection networks called dual-cube extensive networks, denoted by DCEN(G), was introduced recently [4]. It is proved in [4] that DCEN(G) preserves the hamiltonian connectivity and the globally-3*-connectivity of G. In this article, we prove that DCEN(G) "preserves" the edge-pancyclicity of G as well. More precisely, suppose that every edge G lies on a cycle of length l, where l is an arbitrary integer with 3 ≤ l ≤ |G|. Then for any edge ê of DCEN(G), there exists a cycle in DCEN(G), denoted by Cl, such that ê ∈ Cl and the length of Cl is l for every lmin ≤ l ≤ |DCEN(G)|, where lmin ∈ {3, 8}. The result is shown to be optimal. Furthermore, we prove that the similar results hold when G is a bipartite graph.