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Panconnectivity and edge-pancyclicity of 3-ary N-cubes

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Abstract

We study two topological properties of the 3-ary n-cube Q 3 n . Given two arbitrary distinct nodes x and y in Q 3 n , we prove that there exists an x–y path of every length ranging from d(x,y) to 3n−1, where d(x,y) is the length of a shortest path between x and y. Based on this result, we prove that Q 3 n is edge-pancyclic by showing that every edge in Q 3 n lies on a cycle of every length ranging from 3 to 3n.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan, 70101, Taiwan

    Sun-Yuan Hsieh & Tsong-Jie Lin

  2. Department of Information Management, Southern Taiwan University of Technology, No. 1, Nantai Street, Yung-Kang City, Taiwan, 710, Taiwan

    Hui-Ling Huang

Authors
  1. Sun-Yuan Hsieh
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  2. Tsong-Jie Lin
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  3. Hui-Ling Huang
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Correspondence to Sun-Yuan Hsieh.

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Hsieh, SY., Lin, TJ. & Huang, HL. Panconnectivity and edge-pancyclicity of 3-ary N-cubes. J Supercomput 42, 225–233 (2007). https://doi.org/10.1007/s11227-007-0133-5

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  • DOI: https://doi.org/10.1007/s11227-007-0133-5

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