Conditional edge-fault pancyclicity of augmented cubes

Abstract

The augmented cube AQn, proposed by Choudum and Sunitha [7], is a variation of the hypercube Qn 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 2n 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.ʼs result in terms of the number of fault-tolerant edges.