Conditional edge-fault pancyclicity of augmented cubes

The augmented cube AQ(n) proposed by Choudum and Sunitha [7], is a variation of the hypercube Q(n) and possesses many superior properties that the hypercube does not contain. In this paper, we show that, any n-dimensional augmented cube with at most 4n - 12 faulty edges contains cycles of lengths from 3 to 2(n) under the condition that every node is incident with at least two fault-free edges, where n >= 3. Ma et al. [21] obtained the same result but with the number of faulty edges up to 2n - 3. Our result improves Ma et al.'s result in terms of the number of fault-tolerant edges. (C) 2013 Elsevier B.V. All rights reserved.