Abstract: With the semi-direct product of groups，several schemes for designing interconnection networks with constant degree are unified under a general framework theoretically.A new family of Cayley graph，called CSC（q，p，l，k） is introduced based on this general framework，which shows a better scalability.This paper verifies that CSC（q，p，l，k） includes some well-known significant multistage interconnection networks as its subclasses，for example，Cube-Connected Cycles（CCC），the k-degree Cayley graph recently proposed.This work can induce computer designers to obtain desired network by a proper choice of parameters such that it is attractive for some applications like parallel architecture and P2P overlay system.A unified framework of Cayley graph can avoid to repeatedly exploit some “new” interconnection networks.

Key words: semi-direct product, Cayley graph, multistage networks

摘要： 使用群论中的半直积作为工具，将已有的若干构建互连网络的方法统一成一种Cayley图模型CSC（q，p，l，k），使其具有更好的可扩展性。并证明了CSC（q，p，l，k）网络包括了若干重要的互连网络作为它的特殊情形，例如立方连通圈、星连通圈和最近提出并受到关注的k度Cayley图。提出该模型的意义在于为计算机系统的设计者们提供只需要选择合适的参数就可以确定自己需要的互连网络模型。其次，该模型也在一定程度上避免一些在互连网络构建方面的冗余研究工作。

关键词: 半直积, 凯莱图, 多级网络