Cycle and path embedding on 5-ary N-cubes

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

doi:10.1051/ita:2008004

Lin, Tsong-Jie ; Hsieh, Sun-Yuan ; Huang, Hui-Ling ¹

¹ Department of Information Management, Southern Taiwan University, No. 1, NanTai Street, Tainan 71005, Taiwan;

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 133-144

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 $5^{n}$ .

MR Zbl

DOI : 10.1051/ita:2008004

Classification : 68R10, 68R05, 05C12
Keywords: graph-theoretic interconnection networks, hypercubes, $k$-ary $n$-cubes, panconnectivity, edge-pancyclicity

Affiliations des auteurs :

Lin, Tsong-Jie ; Hsieh, Sun-Yuan ; Huang, Hui-Ling ¹

¹ Department of Information Management, Southern Taiwan University, No. 1, NanTai Street, Tainan 71005, Taiwan;

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     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},
     pages = {133--144},
     year = {2009},
     publisher = {EDP Sciences},
     volume = {43},
     number = {1},
     doi = {10.1051/ita:2008004},
     mrnumber = {2483447},
     zbl = {1156.68041},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita:2008004/}
}

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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) no. 1, pp. 133-144. doi: 10.1051/ita:2008004

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