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Zbl 1156.68041
Lin, Tsong-Jie; Hsieh, Sun-Yuan; Huang, Hui-Ling
Cycle and path embedding on 5-ary $n$-cubes. (English)
[J] Theor. Inform. Appl. 43, No. 1, 133-144 (2009). ISSN 0988-3754; ISSN 1290-385X/e

Summary: 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 $5^n-1$, where $n\geq 2$. 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 $5^n$.

MSC 2000:: *68R10 Graph theory in connection with computer science
05C10 Topological graph theory
05C38 Paths and cycles

Keywords: graph-theoretic interconnection networks; hypercubes; $k$-ary $n$-cubes; panconnectivity; edge-pancyclicity

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