Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges

  • Authors:

  • Sun-Yuan Hsieh;Nai-Wen Chang

  • Affiliations:

  • IEEE;-

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 2006

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Abstract

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 F_{v} and F_{e} be the sets of faulty nodes and faulty edges of an n{\hbox{-}}{\rm dimensional} Möbius cube MQ_{n}, respectively, and let F=F_{v}\cup F_{e}. A faulty graph is pancyclic if it contains fault-free cycles of all lengths from 4 to |V-F_{v}|. In this paper, we show that MQ_{n}-F contains a fault-free Hamiltonian path when |F|\leq n-1 and n\geq 1. We also show that MQ_{n}-F is pancyclic when |F|\leq n-2 and n\geq 2. Since MQ_{n} is regular of degree n, both results are optimal in the worst case.