Star fault tolerance of hypercube

Abstract

In this paper, first we estimate the star conditional connectivity of Hypercube, where the star conditional connectivity is the minimum number of stars in a graph, such that the deletion of those stars disconnects the graph and the left graph has property P. Second, a graph is called strongly Menger connected if for any two vertices u,v in the graph, there are min(d(u),d(v)) internally disjoint paths between them, where d(u),d(v) are the degree of u,v in the graph. In this paper, we propose k-star-fault-tolerance strong Menger connectivity. A graph is called k-star-fault-tolerance strong Menger connected if after the removal of no more that k stars, the left graph remains strongly Menger connected. We show that Hypercube Qn is ⌊n−22⌋-star-fault-tolerance strongly Menger connected. Moreover, the bound is sharp.