Path bipancyclicity of hypercubes

  • Authors:
  • Chang-Hsiung Tsai;Shu-Yun Jiang

  • Affiliations:
  • Institute of Learning Technology, National Hualien University of Education, Hualien, Taiwan 970, ROC;Institute of Learning Technology, National Hualien University of Education, Hualien, Taiwan 970, ROC

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

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Abstract

A bipartite graph is vertex-bipancyclic (respectively, edge-bipancyclic) if every vertex (respectively, edge) lies in a cycle of every even length from 4 to |V(G)| inclusive. It is easy to see that every connected edge-bipancyclic graph is vertex-bipancyclic. An n-dimensional hypercube, or n-cube denoted by Q"n, is well known as bipartite and one of the most efficient networks for parallel computation. In this paper, we study a stronger bipancyclicity of hypercubes. We prove that every n-dimensional hypercube is (2n-4)-path-bipancyclic for n=3. That is, for any path P of length k with 1==3.