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.

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 n2. 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 .

DOI : 10.1051/ita:2008004
Classification : 68R10, 68R05, 05C12
Mots-clés : graph-theoretic interconnection networks, hypercubes, $k$-ary $n$-cubes, panconnectivity, edge-pancyclicity
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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     title = {Cycle and path embedding on 5-ary {N-cubes}},
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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. http://archive.numdam.org/articles/10.1051/ita:2008004/

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