Component connectivity of augmented cubes

Abstract

Classical connectivity is a vital metric to explore fault tolerance and reliability of network-based multiprocessor systems. The component connectivity is a more advanced metric to assess the fault tolerance of network structures beyond connectivity and has gained great progress. For a non-complete graph G=(V(G),E(G)), a subset T⊆V(G) is called an r-component cut of G, if G−T is disconnected and has at least r components (r≥2). The r-component connectivity of G, denoted by cκr(G), is the cardinality of the minimum r-component cut. The component connectivities of some networks for small r have been determined, while some progresses for large r only focus on the networks which take hypercube as their modules. In this paper, we determine the (r+1)-component connectivity of augmented cubes cκr+1(AQn)=2nr−4r−(r2)+3, for n≥13, 6≤r≤⌊n−12⌋, and particularly cκr+1(AQn)=2nr−4r−(r2)+2 for n≥5, r∈{4,5}.