A cycle structure theorem for Hamiltonian graphs
Journal of Combinatorial Theory Series A
A recursively scalable network VLSI implementation
Future Generation Computer Systems
An optimized broadcasting technique for WK-Recursive topologies
Future Generation Computer Systems - Improving perfomance in multiprocessors and networks
Pancyclism and bipancyclism of Hamiltonian graphs
Journal of Combinatorial Theory Series B
Parallel algorithms for regular architectures: meshes and pyramids
Parallel algorithms for regular architectures: meshes and pyramids
A note on the minimum size of a vertex pancyclic graph
Selected papers from the second Krakow conference on Graph theory
Journal of Combinatorial Theory Series B
Analytical Modeling of Wormhole-Routed k-Ary n-Cubes in the Presence of Hot-Spot Traffic
IEEE Transactions on Computers
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
Interconnection Networks: An Engineering Approach
Interconnection Networks: An Engineering Approach
On pancyclism in hamiltonian graphs
Discrete Mathematics
Rotator Graphs: An Efficient Topology for Point-to-Point Multiprocessor Networks
IEEE Transactions on Parallel and Distributed Systems
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Multicast communication in wormhole-routed symmetric networks with hamiltonian cycle model
Journal of Systems Architecture: the EUROMICRO Journal
On Some Combinatorial Properties of the Star Graph
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
The WK-Recursive Pyramid: An Efficient Network Topology
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
The algorithm of pipelined gossiping
Journal of Systems Architecture: the EUROMICRO Journal
The Grid-Pyramid: A Generalized Pyramid Network
The Journal of Supercomputing
Hamiltonian Connectedness of the Faulty WK-Recursive Network
PDCAT '06 Proceedings of the Seventh International Conference on Parallel and Distributed Computing, Applications and Technologies
Journal of Graph Theory
The triangular pyramid: Routing and topological properties
Information Sciences: an International Journal
Nonflat surface level pyramid: a high connectivity multidimensional interconnection network
The Journal of Supercomputing
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The WK-recursive mesh and WK-pyramid networks are recursively defined hierarchical interconnection networks with excellent properties which well idealize them as alternatives for mesh and traditional pyramid interconnection topologies. They have received much attention due to their favorable attributes such as small diameter, large connectivity, and high degree of scalability and expandability. In this paper, we deal with pancyclicity and surface area of these networks. These properties are of great importance in the implementation of a variety of parallel algorithms in multicomputers. We show that WK-recursive mesh network is 1-partially pancyclic, i.e. any cycle of length 3, 4, 6,..., and N can be constructed in the WK-recursive mesh. Also, we prove that the WK-pyramid is pancyclic, that is all cycles of length 3, 4,..., and N can be formed in a WK-pyramid. It is also proved that two link-disjoint Hamiltonian paths/cycles can be embedded in the WK-recursive mesh/WK-pyramid. We then study the surface area of WK-recursive mesh and WK-pyramid networks and put forth some equations for calculating the surface area in these networks.