Weak-vertex-pancyclicity of (n, k)-star graphs

  • Authors:

  • Ying-You Chen;Dyi-Rong Duh;Tai-Ling Ye;Jung-Sheng Fu

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Chi Nan University, No. 1, University Rd., Puli, Nantou Hsien, 54561, Taiwan;Department of Computer Science and Information Engineering, National Chi Nan University, No. 1, University Rd., Puli, Nantou Hsien, 54561, Taiwan;Department of Computer Science and Information Engineering, National Chi Nan University, No. 1, University Rd., Puli, Nantou Hsien, 54561, Taiwan;Department of Electronic Engineering, National United University, Taiwan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

The (n,k)-star graph (S"n","k for short) is an attractive alternative to the hypercube and also a generalized version of the n-star. It is isomorphic to the n-star (n-complete) graph if k=n-1 (k=1). Jwo et al. have already demonstrated in 1991 that an n-star contains a cycle of every even length from 6 to n!. This work shows that every vertex in an S"n","k lies on a cycle of length l for every 3@?l@?n!/(n-k)! when 1@?k@?n-4 and n=6. Additionally, for n-3@?k@?n-2, each vertex in an S"n","k is contained in a cycle of length ranged from 6 to n!/(n-k)!. Moreover, each constructed cycle of an available length in an S"n","k can contain a desired 1-edge.