Abstract
Given a connected subgraph H of an interconnection network G, the H-structure connectivity κ(G;H) and the H-substructure connectivity κs(G;H) of G are two important measurements for fault tolerance of G. The n-dimensional star graph Sn is an attractive interconnection network candidate for multiprocessor systems, and it is (n−1)-regular. Let n≥4 and 0≤r≤n−1. In this paper, we prove that (i)κ(Sn;K1,r)=κs(Sn;K1,r)=n−1, and (ii) the removal of any minimum K1,r-cut (or, minimum sub-K1,r-cut) will split Sn into exactly two components, one of which is a singleton, where K1,r is a tree on 1+r vertices, r of which are leaves. The main results generalize some known ones.
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