Cycle and path embedding on 5-ary N-cubes

Lin, Tsong-Jie; Hsieh, Sun-Yuan; Huang, Hui-Ling

Lin, Tsong-Jie ; Hsieh, Sun-Yuan ; Huang, Hui-Ling

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009), p. 133-144 / Harvested from Numdam

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Résumé

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 $5^{n}$ .

Publié le : 2009-01-01

MR 2483447 | Zbl 1156.68041

DOI : https://doi.org/10.1051/ita:2008004
Classification: 68R10, 68R05, 05C12

@article{ITA_2009__43_1_133_0,
     author = {Lin, Tsong-Jie and Hsieh, Sun-Yuan and Huang, Hui-Ling},
     title = {Cycle and path embedding on 5-ary N-cubes},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {43},
     year = {2009},
     pages = {133-144},
     doi = {10.1051/ita:2008004},
     mrnumber = {2483447},
     zbl = {1156.68041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2009__43_1_133_0}
}

Lin, Tsong-Jie; Hsieh, Sun-Yuan; Huang, Hui-Ling. Cycle and path embedding on 5-ary N-cubes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) pp. 133-144. doi : 10.1051/ita:2008004. http://gdmltest.u-ga.fr/item/ITA_2009__43_1_133_0/

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