A graph G = (V,E) is said to be pancyclic if it contains fault-free cycles of all lengths from 4 to V in G. Let Fv and e be the sets of faulty nodes and faulty edges of an n-dimensional Möbius cube MQn, respectively, and let F = Fv ∪ Fe. A faulty graph is pancyclic if it contains fault-free cycles of all lengths from 4 to V - Fv . In this paper, we show that MQn - F contains a fault-free Hamiltonian path when F ≤ n - 1 and n ≥ 1. We also show that MQn - F is pancyclic when F ≤ n - 2 and n ≥ 2. Since MQn is regular of degree n, both results are optimal in the worst case.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics