Edge-bipancyclicity of star graphs with faulty elements

  • Authors:

  • Chao-Wen Huang;Hui-Ling Huang;Sun-Yuan Hsieh

  • Affiliations:

  • National Center for High-Performance Computing (Taichung Branch), No. 22, Keyuan Rd., Central Taiwan Science Park, Taichung 40763, Taiwan;Department of Information Management, Southern Taiwan University, No. 1, Nantai St, Yung-Kang City, Tainan 710, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, Taiwan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

In this paper, we investigate the fault-tolerant edge-bipancyclicity of an n-dimensional star graph S"n. Given a set F comprised of faulty vertices and/or edges in S"n with |F|@?n-3 and any fault-free edge e in S"n-F, we show that there exist cycles of every even length from 6 to n!-2|F"v| in S"n-F containing e, where n=3. Our result is optimal because the star graph is both bipartite and regular with the common degree n-1. The length of the longest fault-free cycle in the bipartite S"n is n!-2|F"v| in the worst case, where all faulty vertices are in the same partite set. We also provide some sufficient conditions from which longer cycles with length from n!-2|F"v|+2 to n!-2|F"v| can be embedded.