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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 $2 n$ 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 $5^{n}$ .

Cycle and Path Embedding on 5-ary N-cubes

Tsong-Jie Lin, Sun-Yuan Hsieh, Hui-Ling Huang (2008)

RAIRO - Theoretical Informatics and Applications

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.

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Clustering in trees: Optimizing cluster sizes and number of subtrees.

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Combinatorics of singly-repairable families.

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Counting subwords in a partition of a set.

Cycle and path embedding on 5-ary N-cubes

Cycle and Path Embedding on 5-ary N-cubes

Currently displaying 1 – 7 of 7