Pancyclicity on Möbius cubes with maximal edge faults

  • Authors:

  • Sun-Yuan Hsieh;Chun-Hua Chen

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, Ta-Hsueh Road, Tainan 701, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, Ta-Hsueh Road, Tainan 701, Taiwan

  • Venue:
  • Parallel Computing
  • Year:
  • 2004

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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 Fe be the set of faulty edges. In this paper, we show that an n-dimensional Möbius cube, n ≥ 1, contains a fault-free Hamiltonian path when |Fe| ≤ n - 1. We also show that an n- dimensional Möbius cube, n ≥ 2, is pancyclic when |Fe| ≤ n - 2. Since an n-dimensional Möbius cube is regular of degree n, both results are optimal in the worst case.