Edge-fault-tolerant vertex-pancyclicity of augmented cubes

Abstract

The n-dimensional augmented cube, denoted as AQ n , a variation of the hypercube, possesses some properties superior to those of the hypercube. In this paper, we show that every vertex in AQ n lies on a fault-free cycle of every length from 3 to 2 n , even if there are up to n − 1 edge faults. We also show that our result is optimal.