Processor allocation in an N-cube multiprocessor using gray codes
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
IEEE Transactions on Parallel and Distributed Systems
Folded Petersen Cube Networks: New Competitors for the Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Topological properties of hierarchical cubic networks
Journal of Systems Architecture: the EUROMICRO Journal
Parallel computation: models and methods
Parallel computation: models and methods
Comments on "Hierarchical Cubic Networks"
IEEE Transactions on Parallel and Distributed Systems
Topological properties of twisted cube
Information Sciences—Informatics and Computer Science: An International Journal
Embedding of Cycles in Arrangement Graphs
IEEE Transactions on Computers
Embedding Graphs onto the Supercube
IEEE Transactions on Computers
Embedding Hamiltonian Paths in Faulty Arrangement Graphs with the Backtracking Method
IEEE Transactions on Parallel and Distributed Systems
Properties and Performance of Folded Hypercubes
IEEE Transactions on Parallel and Distributed Systems
The Hierarchical Hypercube: A New Interconnection Topology for Massively Parallel Systems
IEEE Transactions on Parallel and Distributed Systems
Algorithms and Properties of a New Two-Level Network with Folded Hypercubes as Basic Modules
IEEE Transactions on Parallel and Distributed Systems
Combinatorial Properties of Hierarchical Cubic Networks
ICPADS '01 Proceedings of the Eighth International Conference on Parallel and Distributed Systems
Wirelength of 1-fault hamiltonian graphs into wheels and fans
Information Processing Letters
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We show that the hierarchical cubic network, an alternative to the hypercube, is hamiltonian-connected using Gray codes. A network is hamiltonian-connected if it contains a hamiltonian path between every two distinct nodes. In other words, a hamiltonian-connected network can embed a longest linear array between every two distinct nodes with dilation, congestion, load, and expansion equal to one. We also show that the hierarchical cubic network contains cycles of all possible lengths but three and five. Since the hypercube contains cycles only of even lengths, it is concluded that the hierarchical cubic network is superior to the hypercube in hamiltonicity. Our results can be applied to the hierarchical folded-hypercube network as well.