Hyper star fault tolerance of bubble sort networks

Abstract

Let H and M be two connected subgraphs of an interconnection network G. If the removal of any minimum H-structure-cut (resp. minimum H-substructure-cut) splits G into exactly two components, one of which is isomorphic to M, then G is said to be hyperH|M-connected (resp. hyper sub-H|M-connected). The bubble sort graph Bn is one of alternative interconnection networks for multiprocessor systems. Let n≥7 and 2≤r≤4. Denote by K1 the complete graph on one vertex and denote by K1,r a star on 1+r vertices. In this paper, we prove that (i) both the K1,r-structure connectivity and the sub-K1,r-structure connectivity of Bn are ⌈n−12⌉; and (ii)Bn is hyper K1,r|K1-connected and hyper sub-K1,r|K1-connected.