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, the authors extend these known group semidirect product constructions via a general algebraic construction based on group semidirect product. They 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, their 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 .