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Cycle and Path Embedding on 5-ary N-cubes
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- Journal:
- RAIRO - Theoretical Informatics and Applications / Volume 43 / Issue 1 / January 2009
- Published online by Cambridge University Press:
- 28 February 2008, pp. 133-144
- Print publication:
- January 2009
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- Article
- Export citation
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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.
