| Issue |
RAIRO-Theor. Inf. Appl.
Volume 43, Number 1, January-March 2009
|
|
|---|---|---|
| Page(s) | 133 - 144 | |
| DOI | https://doi.org/10.1051/ita:2008004 | |
| Published online | 28 February 2008 | |
Cycle and Path Embedding on 5-ary N-cubes
1
Department of Computer Science and Information Engineering,
National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan; tsong0215@yahoo.com.tw
hsiehsy@mail.ncku.edu.tw
2
Department of Information Management,
Southern Taiwan University,
No. 1, NanTai Street, Tainan 71005, Taiwan;
hlhuang@mail.stut.edu.tw
Received:
3
May
2007
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
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