Further Properties of Cayley Digraphs and Their Applications to Interconnection Networks

In this short communication, we extend the known relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups and obtain some general results on homomorphism and distance between them. Intuitively, our results correspond to synthesizing alternative, more economical, interconnection networks by reducing the number of dimensions and/or link density of existing networks via mapping and pruning. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes.