Pancyclicity and bipancyclicity of conditional faulty folded hypercubes

  • Authors:

  • Che-Nan Kuo;Sun-Yuan Hsieh

  • Affiliations:

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

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

A graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive; and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order. The pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network's topology can simulate rings of various lengths. An n-dimensional folded hypercube FQ"n is an attractive variant of an n-dimensional hypercube Q"n that is obtained by establishing some extra edges between the vertices of Q"n. FQ"n for any odd n is known to be bipartite. In this paper, we explore the pancyclicity and bipancyclicity of FQ"n. For any FQ"n (n=2) with at most 2n-3 faulty edges, where each vertex is incident to at least two fault-free edges, we prove that there exists a fault-free cycle of every even length from 4 to 2^n; and when n=2 is even, we prove there also exists a fault-free cycle of every odd length from n+1 to 2^n-1. The result is optimal with respect to the number of faulty edges tolerated.