UPSI Digital Repository (UDRep)
Start | FAQ | About

QR Code Link :

Type :article
Subject :L Education (General)
ISSN :0094243X
Main Author :Chien, S. L. E.
Additional Authors :Raja Noor Farah Azura Raja Maamor Shah
M. Othman
Title :A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks (IR)
Year of Publication :2017
PDF Full Text :Click to view PDF file

Abstract :
The performance parameters and properties of chordal rings have been researched extensively as models for parallel and distributed interconnection topology models since their founding in 1981. A chordal ring is modelled after a circulant graph, where its vertices represent processor nodes and its edges represent the links between them. Hence, its performance and properties of connectivity can be studied through graph theory. This research was aimed at the investigation of a new degree six chordal ring, the optimised degree six 3-modified chordal ring CHR6o3. A tree visualisation was constructed based on its connectivity to enable the generation of formulae for optimal diameter and average optimal path lengths. As the numbers of nodes further increased with its layers, the visualisation was found to be more accurately represented in a table where all the combinations of different links for each node were listed, compared to drawing it out. Redundant nodes were also more easily found by using this representation. Furthermore, the 'snowflake' geometrical representation was proposed to illustrate the connectivity of nodes in CHR6o3 as well as to aid the proving of some properties involving its Hamiltonicity. The results of this research are important in developing a routing algorithm for CHR6o3.


1. Lee, H. Analysis of Chordal Ring Network (1981) IEEE Transactions on Computers, C-30 (4), pp. 291-295. Cited 188 times. doi: 10.1109/TC.1981.1675777 2. Browne, R.F., Hodgson, R.M. Symmetric degree-four chordal ring networks (1990) IEE Proceedings E: Computers and Digital Techniques, 137 (4), pp. 310-318. Cited 13 times. doi: 10.1049/ip-e.1990.0038 3. Matroud, A.A. (2006) Ph.D. thesis, Universiti Putra Malaysia, Malaysia 4. Bujnowski, S., Dubalski, B., Zabłudowski, A., Pedersen, J.M., Riaz, T. Analysis of degree 5 chordal rings for network topologies (2011) Advances in Intelligent and Soft Computing, 102, pp. 445-457. Cited 6 times. ISBN: 978-364223153-7 doi: 10.1007/978-3-642-23154-4_49 5. Azura, R.N.F., Othman, M., Selamat, M.H., Peng, Y.H. (2008) Proceedings of Simposium Kebangsaan Sains Matematik ke-16, pp. 515-522. Cited 8 times. 6. Bujnowski, S., Dubalski, B., Zabłudowski, A., Ledźinski, D., Marciniak, T., Pedersen, J.M. Comparison of modified degree 6 chordal rings (2010) Advances in Intelligent and Soft Computing, 84, pp. 435-445. Cited 4 times. ISBN: 978-364216294-7 doi: 10.1007/978-3-642-16295-4_49 7. Irwan, N., Farah, R.N., Sofi, A.Z.M. (2010) Proceedings of the International Conference on Intelligent Network and Computing, pp. 16-20. Cited 2 times. 8. Dubalski, B., Bujnowski, S., Ledziński, D., Zabłudowski, A., Kiedrowski, P. (2012) New Frontiers in Graph Theory, p. 43. Cited 4 times. edited by Y. Zhang (InTech, China) 9. Ledziński, D., Bujnowski, S., Marciniak, T., Pedersen, J.M., Lopez, J.G. Network structures constructed on basis of chordal rings 4th degree (2014) Advances in Intelligent Systems and Computing, 233, pp. 281-299. Cited 3 times. ISBN: 978-331901621-4 doi: 10.1007/978-3-319-01622-1_33 10. Barrière, L. (2003) Discrete Applied Mathematics, 129, pp. 211-232. Cited 8 times. 11. Azura, R.N.F., Othman, M., Hock, P.Y., Selamat, M.H. On properties of modified degree six chordal rings network (2010) Malaysian Journal of Mathematical Sciences, 4 (2), pp. 147-157. Cited 5 times.

This material may be protected under Copyright Act which governs the making of photocopies or reproductions of copyrighted materials.
You may use the digitized material for private study, scholarship, or research.

Back to previous page

Installed and configured by Bahagian Automasi, Perpustakaan Tuanku Bainun, Universiti Pendidikan Sultan Idris
If you have enquiries with this repository, kindly contact us at or Whatsapp +60163630263 (Office hours only)