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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  1. S.G. Akl, Parallel Computation: Models and Methods Prentice Hall, NJ (1997).  
  2. S. Borkar, R. Cohn, G. Cox, S. Gleason, T. Gross, H.T. Kung, M. Lam, B. Moore, C. Peterson, J. Pieper, L. Rankin, P.S. Tseng, J. Sutton, J. Urbanski and J. Webb, iWarp: an integrated solution to high-speed parallel computing, Proceedings of the 1988 ACM/IEEE conference on Supercomputing (1988) 330–339.  
  3. B. Bose, B. Broeg, Y.G. Kwon and Y. Ashir, Lee distance and topological properties of k-ary n-cubes. IEEE Trans. Comput.44 (1995) 1021–1030.  
  4. J. Chang, J. Yang and Y. Chang, Panconnectivity, fault-Tolorant Hamiltonicity and Hamiltonian-connectivity in alternating group graphs. Networks44 (2004) 302–310.  
  5. K. Day and A.E. Al-Ayyoub, Fault diameter of k-ary n-cube Networks. IEEE Transactions on Parallel and Distributed Systems, 8 (1997) 903–907.  
  6. S.A. Ghozati and H.C. Wasserman, The k-ary n-cube network: modeling, topological properties and routing strategies. Comput. Electr. Eng. (2003) 1271–1284.  
  7. S.Y. Hsieh, T.J. Lin and H.-L. Huang, Panconnectivity and edge-pancyclicity of 3-ary N-cubes. J. Supercomputing42 (2007) 225–233.  
  8. F.T. Leighton, Introduction to Parallel Algorithms and Architecture: Arrays . Trees . Hypercubes. Morgan Kaufmann, San Mateo, CA (1992).  
  9. M. Ma and J. M. Xu, Panconnectivity of locally twisted cubes. Appl. Math. Lett.19 (2006) 673–677.  
  10. B. Monien and H. Sudborough, Embedding one interconnection network in another. Computing Suppl.7 (1990) 257–282.  
  11. W. Oed, Massively parallel processor system CRAY T3D. Technical Report, Cray Research GmbH (1993).  
  12. A.L. Rosenberg, Cycles in Networks. Technical Report: UM-CS-1991-020, University of Massachusetts, Amherst, MA, USA (1991).  
  13. C.L. Seitz et al., Submicron systems architecture project semi-annual technical report. Technical Report Caltec-CS-TR-88-18, California Institute of Technology (1988).  
  14. Y. Sheng, F. Tian and B. Wei, Panconnectivity of locally connected claw-free graphs. Discrete Mathematics203 (1999) 253–260.  
  15. Z.M. Song and Y.S. Qin, A new sufficient condition for panconnected graphs. Ars Combinatoria34 (1992) 161–166.  
  16. D. Wang, T. An, M. Pan, K. Wang and S. Qu, Hamiltonian-like properies of k-Ary n-Cubes, in Proceedings PDCAT05 of Sixth International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT05), IEEE Computer Society Press (2005) pp. 1002–1007.  

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