Subnetwork preclusion for bubble-sort networks

Abstract

For two positive integers n and m with n>m, the Gn−m preclusion node (resp. link) number Fm(Gn) (resp. fm(Gn)) of an n-dimensional interconnection network Gn is the minimum number of nodes (resp. links), if any, whose deletion results in a network with no subnetwork isomorphic to Gn−m. The n-dimensional bubble-sort network Bn is one of the most attractive interconnection networks for multiprocessor systems. In this paper, we prove that F2(Bn)=f2(Bn)=n(n−1) for n≥6.