Product-closed networks

We present a uniform mathematical characterization of interconnection network classes referred to as product-closed networks (PCN). A number of popular network classes fall under this characterization including binary hypercubes, tori, k-ary n-cubes, meshes, and generalized hypercubes. An unlimited number of other networks can be defined using the presented mathematical characterization. An important common feature for all PCN classes is their closure under the Cartesian product of graphs. This provides a tool for generating new PCN classes of interconnection graphs. We evaluate a number of commonly used metrics for all PCN networks including the size, degree, diameter, average distance, connectivity, and fault diameter. We show how all PCN networks share various desirable properties such as simple distributed routing, hierarchical structure, complete sets of node-disjoint paths between arbitrary nodes, attractive embeddings, distributed broadcasting, and fault tolerance properties. The proposed characterization provides a unified model for representing and further analyzing the various known PCN networks, and for building new ones with predetermined properties and characteristics. Keywordsbroadcasting, Cartesian product of graphs, embedding, hierarchical structure, interconnection networks, node-disjoint paths, routing.