The authors develop a formal group-theoretic model, called the Cayley graph model, for designing, analyzing, and improving such networks. They show that this model is universal and demonstrate how interconnection networks can be concisely represented in this model. It is shown that this model enables the authors to design networks based on representations of finite groups. They can then analyze these networks by interpreting the group-theoretic structure graph theoretically, Using these ideas, and motivated by certain well-known combinatorial problems, they develop two classes of networks called star graphs and pancake graphs. These networks are shown to have better performance than previous networks. >

This paper investigates group graphs as a source of interconnection networks. It is shown that while these graphs possess many properties desirable in all interconnection networks, their diversity allows the generation of interconnection networks which may be optimized with regard to a variety of specific parameters. Techniques are described for generating, combining, and analyzing these graphs with respect to their order, diameter, fault tolerance, etc. A theorem is derived which shows that a large important class of group graphs are optimally fault tolerant. A number of examples are included.