Principle of Symmetry for Network Topology with Applications to Some Networks

A number of Cayley-graph interconnection structures, such as cube-connected cycles, butterfly and biswapped networks, are known to be derivable by unified group semidirect product construction. In this paper, we extend these known group semidirect product constructions via a general algebraic construction based on group semidirect product. We show that under certain conditions, graphs based on the constructed groups are also Cayley graphs when graphs of the original groups are Cayley graphs. Thus, our results present a general mathematical framework-symmetry for synthesizing and exploring interconnection networks that offer many excellent properties such that  lower node degrees, and thus smaller VLSI layout and simpler physical packaging of the same size and lower diameters, and thus lower delay of networks . Our constructions also lead to new insights, as well as new concrete results, for previously known interconnection schemes such as cube-connected cycles and biswapped networks.