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

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 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.

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 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 -

References

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