Subnetwork Preclusion of (n, k)-Star Networks

Abstract

The [Formula: see text]-star graph [Formula: see text], which is introduced to address scaling issues of the star graph, is recognized as an attractive interconnection network topology for building multiprocessor systems because of its desirable properties. Let [Formula: see text] be the minimum number of faulty vertices that make every subgraph isomorphic to [Formula: see text] faulty in [Formula: see text] under vertex-failure model, where [Formula: see text]. In this paper, we prove that [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] and [Formula: see text].