Incomplete Star: An Incrementally Scalable Network Based on the Star Graph

Abstract

We introduce a new interconnection network for massively parallel systems called the incomplete star graph. We describe unique ways of interconnecting and labeling the nodes and routing point-to-point communications within this network. In addition, we provide an analysis of a special class of incomplete star graph called C n-1 graph and obtain the diameter and average distance for this network. For the C n-1 graph, an efficient broadcasting scheme is presented. Furthermore, it is proven that a C n-1 with N nodes (i.e., N = m(n − 1)!) is Hamiltonian if m=4 or m=3k, and k ≠ 2. © 1994 IEEE