Cluster model for optimal double-loop connected network

This paper investigates the solution of the optimization problem that appears in the design of double loop structured local area computer networks or interconnection networks. Double loop structure is a regular, two-connected network, designed for packet communications. The studies of degree two network connection schemes is based on the circular graphs of degree four. These graphs are regular, vertex-symmetric, and maximally connected, and such optimal graph exists for any given number of nodes. Every four of two-connected nodes consists a cluster, so cluster is a component with four input and four output link in the network. The proposed cluster network forms the optimal connection of a circular graph. We demonstrate how to construct one such network for any number of nodes and examine their network properties. The problem of routing is also addressed, and two routing rules are investigated that take advantage of the network regular structure.<>