Component connectivity of augmented cubes

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 subset of 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 c kappa(r)(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 c kappa(r+1)(AQ(n)) = 2nr - 4r - ((r)(2)) + 3, for n >= 13, 6 <= r <= left perpendicularn-1/2right perpendicular, and particularly c kappa(r+1) (AQ(n)) = 2nr - 4r - ((r)(2)) + 2 for n >= 5, r is an element of {4, 5}. (c) 2023 Elsevier B.V. All rights reserved.