Abstract: An interconnection network is an important partite of a supercomputer．In 1989,S.B．Akers et al,proposed a group-theoretic model for interconnection networks and designed many interconnection networks,such as,star network,bubble sort network,etc．In particularly,star networks own many better performances than the popular n-cubes．However,they have a weakness:the size of all above networks is n!,that is,n! is very speedly increasing with adding of n．This results in that the scalability of supercomputers built by the interconnection networks is very difficult．That is,the scalability of the supercomputer isn’t good．We proposed a multipartite group-theoretic model based on the the group-theoretic model．By this model,we designed many interconnection networks,such as,(n,k)-multipartite star networks,(n,k)-bubble sort networks,etc．Furthermore,we showed star network is(n,1)-multipartite star network and(n,k)-multipartite star networks own following better performances:the size of the network increases with fixed increment,its diameter increases slowly,its dgree is fixed．Other(n,k)-multipartite networks designed here own also the performances.

Key words: Interconnection network,Star network,n-cube,(n,k)-multipartite cayley graph,(n,k)-multipartite star network