Conditional connectivity of recursive interconnection networks respect to embedding restriction ?
Large-scale multiprocessor systems always take some recursive interconnection networks as underlying topologies. Let Gn G n be an n-dimensional recursive interconnection network. The m -embedding-restricted connectivity ?m(Gn) ? m ( G n ) (resp. the m -embedding-restricted edge connectivity ?m(Gn) ? m ( G n ) ) of Gn G n is the cardinality of a minimum subset of nodes (resp. edges), if any, whose deletion disconnects Gn G n and each node of the remaining components lies in an undamaged m -dimensional sub-network Gm G m . In this paper, we present some relationships between the proposed indices and other conditional connectivity indices in general recursive interconnection networks. We give some bounds on these two indices in k-ary n-cubes and bubble-sort networks. In addition, we determine these two indices in k-ary n-cubes and bubble-sort networks in some cases.
connectivity interconnection network k-ary n-cube bubble-sort network distributed system hypercube