Topological and Communication Aspects of Hyper-Star Graphs

A hyper-star graph HS(m,k) has been introduced as a class of lower cost interconnection networks. Hyper-star graph has more merit than hypercube when degree × diameter is used as a cost measure. In other words, they have smaller degree and diameter than hypercubes. In this paper, we consider some of the important properties of hyper-star graphs such as symmetry, w-diameter, and fault diameter. We show that HS(2n,n) is node-symmetric. We also show that the w-diameter of HS(2n,n) is bounded by the shortest path length plus 4, and fault diameter of HS(2n,n) is bounded by its diameter plus 2. In addition, we introduce an efficient broadcasting scheme in hyper-star graphs based on a spanning tree with minimum height.