Abstract
The Cartesian and Composition products are two well known graph products, also applied to interconnection networks area. The Cartesian and Composition network products possess great characteristics of fault resilience according to their high connectivity. In this paper, we study the existence and construction of parallel routing paths in these two well-known product networks. To prove the existence of certain number of parallel paths in these product networks, we need to compute their connectivity. By assuming the availability of certain number of faulty nodes, we propose some new shortest-path parallel routing algorithms. These algorithms can be used both in faulty networks and to route different data from different paths to a specified target node. We also study the concept of container length and wide diameter of the two mentioned product networks. Comparison between wide diameters and diameters of the two networks exhibit the efficiency of these product networks in constructing node disjoint paths.
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