Structure Fault-tolerance of the Augmented Cube

Abstract

The augmented cube, denoted by , AQ_n is an important variant of the hypercube. It retains many favorable properties of the hypercube and possesses several embeddable properties that the hypercube and its other variations do not possess. Connectivity is one of the most important indicators used to evaluate a network’s fault tolerance performance. Structure and substructure connectivity are the two novel generalizations of the connectivity, which provide a new way to evaluate fault-tolerant ability of a network. In this paper, the structure connectivity and substructure connectivity of the augmented cube for H ∈ {K_(1,m), P_L, C_N} is investigated, where 1 ≤ M ≤ 6, 1 ≤ L ≤ 2n-1 and 3 ≤ N ≤ 2n-1.