# Cycle and path embedding on 5-ary N-cubes

• [1] Department of Information Management, Southern Taiwan University, No. 1, NanTai Street, Tainan 71005, Taiwan;
• Volume: 43, Issue: 1, page 133-144
• ISSN: 0988-3754

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## Abstract

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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 $n\ge 2$. 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 ${5}^{n}$.

## How to cite

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Lin, Tsong-Jie, Hsieh, Sun-Yuan, and Huang, Hui-Ling. "Cycle and path embedding on 5-ary N-cubes." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 43.1 (2009): 133-144. <http://eudml.org/doc/245576>.

@article{Lin2009,
abstract = {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 $n\ge 2$. 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 $5^\{n\}$.},
affiliation = {Department of Information Management, Southern Taiwan University, No. 1, NanTai Street, Tainan 71005, Taiwan;},
author = {Lin, Tsong-Jie, Hsieh, Sun-Yuan, Huang, Hui-Ling},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {graph-theoretic interconnection networks; hypercubes; $k$-ary $n$-cubes; panconnectivity; edge-pancyclicity; -ary -cubes},
language = {eng},
number = {1},
pages = {133-144},
publisher = {EDP-Sciences},
title = {Cycle and path embedding on 5-ary N-cubes},
url = {http://eudml.org/doc/245576},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Lin, Tsong-Jie
AU - Hsieh, Sun-Yuan
AU - Huang, Hui-Ling
TI - Cycle and path embedding on 5-ary N-cubes
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2009
PB - EDP-Sciences
VL - 43
IS - 1
SP - 133
EP - 144
AB - 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 $n\ge 2$. 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 $5^{n}$.
LA - eng
KW - graph-theoretic interconnection networks; hypercubes; $k$-ary $n$-cubes; panconnectivity; edge-pancyclicity; -ary -cubes
UR - http://eudml.org/doc/245576
ER -

## References

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