# Cycle and Path Embedding on 5-ary N-cubes

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

RAIRO - Theoretical Informatics and Applications (2008)

- Volume: 43, Issue: 1, page 133-144
- ISSN: 0988-3754

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topLin, Tsong-Jie, Hsieh, Sun-Yuan, and Huang, Hui-Ling. "Cycle and Path Embedding on 5-ary N-cubes." RAIRO - Theoretical Informatics and Applications 43.1 (2008): 133-144. <http://eudml.org/doc/92902>.

@article{Lin2008,

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 5n - 1, where n ≥ 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 5n.
},

author = {Lin, Tsong-Jie, Hsieh, Sun-Yuan, Huang, Hui-Ling},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Graph-theoretic interconnection
networks; hypercubes; k-ary n-cubes; panconnectivity;
edge-pancyclicity.; graph-theoretic interconnection networks; -ary -cubes; edge-pancyclicity},

language = {eng},

month = {2},

number = {1},

pages = {133-144},

publisher = {EDP Sciences},

title = {Cycle and Path Embedding on 5-ary N-cubes},

url = {http://eudml.org/doc/92902},

volume = {43},

year = {2008},

}

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

DA - 2008/2//

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 5n - 1, where n ≥ 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 5n.

LA - eng

KW - Graph-theoretic interconnection
networks; hypercubes; k-ary n-cubes; panconnectivity;
edge-pancyclicity.; graph-theoretic interconnection networks; -ary -cubes; edge-pancyclicity

UR - http://eudml.org/doc/92902

ER -

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