Hyper-Star Graph: A New Interconnection Network Improving the Network Cost of the Hypercube

In this paper, we introduce the hyper-star graph HS(n, k) as a new interconnection network, and discuss its properties such as faulttolerance, scalability, isomorphism, routing algorithm, and diameter. A hyper-star graph has merits when degree × diameter is used as a desirable quality measure of an interconnection network because it has a small degree and diameter. We also introduce a variation of HS(2k, k), folded hyper-star graphs FHS(2k, k) to further improve the cost degree × diameter of a hypercube: when FHS(2k, k) and an n-dimensional hypercube have the same number of nodes, degree × diameter of FHS(2k, k) is less than (k +1)(⌈logK⌉+1) whereas a hypercube is n2, where K = 2k/ k). It shows that FHS(2k, k) is superior to a hypercube and its variations in terms of the cost, degree × diameter.