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Cycle and Path Embedding on 5-ary N-cubes

Published online by Cambridge University Press:  28 February 2008

Tsong-Jie Lin ,
Sun-Yuan Hsieh  and
Hui-Ling Huang
Tsong-Jie Lin
Affiliation:
Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan; tsong0215@yahoo.com.tw hsiehsy@mail.ncku.edu.tw
Sun-Yuan Hsieh
Affiliation:
Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan; tsong0215@yahoo.com.tw hsiehsy@mail.ncku.edu.tw
Hui-Ling Huang
Affiliation:
Department of Information Management, Southern Taiwan University, No. 1, NanTai Street, Tainan 71005, Taiwan; hlhuang@mail.stut.edu.tw
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Abstract

We study two topological properties of the 5-ary n-cube $Q_{n}^{5}$. Given two arbitrary distinct nodes x and y in $Q_{n}^{5}$, we prove that there exists an x-y path of every length ranging from 2n to 5n - 1, where n ≥ 2. Based on this result, we prove that $Q_{n}^{5}$ is 5-edge-pancyclic by showing that every edge in $Q_{n}^{5}$ lies on a cycle of every length ranging from 5 to 5n.

Keywords

Graph-theoretic interconnection networkshypercubesk-ary n-cubespanconnectivityedge-pancyclicity.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 133 - 144
Copyright
© EDP Sciences, 2008

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