Pancyclicity on Mobius cubes with edge faults

Abstract

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/sub e/ be the set of faulty edges. In this paper, we show that an n-dimensional Mobius cube, n /spl ges/ 1, contains a fault-free Hamiltonian path when |F/sub e/| /spl les/ n-1. We also show that an n-dimensional Mobius cube, n /spl ges/ 2, is pancyclic when |F/sub e/| /spl les/ n-2. Since an n-dimensional Mobius cube is regular of degree n, both results are optimal in the worst case.