Cycle and Path Embedding on 5-ary N-cubes
Department of Computer Science and Information Engineering,
National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan; firstname.lastname@example.org
2 Department of Information Management, Southern Taiwan University, No. 1, NanTai Street, Tainan 71005, Taiwan; email@example.com
Accepted: 22 January 2008
We study two topological properties of the 5-ary n-cube . Given two arbitrary distinct nodes x and y in , 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 is 5-edge-pancyclic by showing that every edge in lies on a cycle of every length ranging from 5 to 5n.
Mathematics Subject Classification: 68R10 / 68R05 / 05C12
Key words: Graph-theoretic interconnection networks / hypercubes / k-ary n-cubes / panconnectivity / edge-pancyclicity.
© EDP Sciences, 2008