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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... 

In this paper, we envision a solution for the problem of capturing an intruder in one of the most popular interconnection topologies, namely the pyramid. A set of agents collaborate to capture a hostile intruder in the network. While the agents can move in the network one hop at a time, the intruder is assumed to be arbitrarily fast, i.e. it can traverse any number of nodes contiguously as far as there are no agents in those nodes. Here we consider a new version of the problem where each agent can replicate new agents when needed, i.e. the algorithm starts with a single agent and new agents are created on demand. In particular, we propose two different algorithms on the pyramid network and...