Pancyclicity on Mobius cubes with 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 ≥ 1, contains a fault-free Hamiltonian path when |F_e| ≤ n-1. We also show that an n-dimensional Mobius cube, n ≥ 2, is pancyclic when |F_e| ≤ n-2. Since an n-dimensional Mobius cube is regular of degree n, both results are optimal in the worst case.