Fault-Tolerant Panconnectivity of Augmented Cubes AQn

Abstract

The augmented cube [Formula: see text] is a variation of the hypercube [Formula: see text]. This paper considers the fault-tolerant Panconnectivity of [Formula: see text]. Assume that [Formula: see text] and [Formula: see text]. We prove that for any two fault-free vertices [Formula: see text] and [Formula: see text] with distance [Formula: see text] in [Formula: see text], there exists a fault-free path [Formula: see text] of each length from [Formula: see text] to [Formula: see text] in [Formula: see text] if [Formula: see text], where [Formula: see text] is the number of faulty vertices in [Formula: see text]. Moreover, the bound is sharp.