Pancyclicity on Mobius cubes with maximal edge faults

A graph G = (V,E) is said to be pancyclic if it contains cycles of all lengths from 4 to \V\ in G. Let F-e be the set of faulty edges. In this paper, we show that an n-dimensional Mobius cube, n greater than or equal to 1, contains a fault-free Hamiltonian path when \F-e\ less than or equal to n - 1. We also show that an n-dimensional Mobius cube, n greater than or equal to 2, is pancyclic when \F-e\ less than or equal to, n - 2. Since an n-dimensional Mobius cube is regular of degree n, both results are optimal in the worst case. (C) 2004 Elsevier B.V. All rights reserved.