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A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks

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 ed...

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Main Authors: Chien, Stephen Lim Een, Raja Maamor Shah, Raja Noor Farah Azura, Othman, Mohamed
Format: Conference or Workshop Item
Language:English
Published: AIP Publishing 2016
Online Access:http://psasir.upm.edu.my/id/eprint/57482/1/A%20%27snowflake%27%20geometrical%20representation%20for%20optimised%20degree%20six%203%E2%80%93modified%20chordal%20ring%20networks.pdf
http://psasir.upm.edu.my/id/eprint/57482/
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spelling my.upm.eprints.574822017-09-27T11:09:11Z http://psasir.upm.edu.my/id/eprint/57482/ A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks Chien, Stephen Lim Een Raja Maamor Shah, Raja Noor Farah Azura Othman, Mohamed 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. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57482/1/A%20%27snowflake%27%20geometrical%20representation%20for%20optimised%20degree%20six%203%E2%80%93modified%20chordal%20ring%20networks.pdf Chien, Stephen Lim Een and Raja Maamor Shah, Raja Noor Farah Azura and Othman, Mohamed (2016) A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks. In: International Conference on Education, Mathematics and Science 2016 (ICEMS2016) in conjunction with 4th International Postgraduate Conference on Science and Mathematics 2016 (IPCSM2016), 19 Nov. 2016, Perak, Malaysia. (pp. 1-6). 10.1063/1.4983860
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description 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.
format Conference or Workshop Item
author Chien, Stephen Lim Een
Raja Maamor Shah, Raja Noor Farah Azura
Othman, Mohamed
spellingShingle Chien, Stephen Lim Een
Raja Maamor Shah, Raja Noor Farah Azura
Othman, Mohamed
A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
author_facet Chien, Stephen Lim Een
Raja Maamor Shah, Raja Noor Farah Azura
Othman, Mohamed
author_sort Chien, Stephen Lim Een
title A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
title_short A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
title_full A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
title_fullStr A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
title_full_unstemmed A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
title_sort 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks
publisher AIP Publishing
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/57482/1/A%20%27snowflake%27%20geometrical%20representation%20for%20optimised%20degree%20six%203%E2%80%93modified%20chordal%20ring%20networks.pdf
http://psasir.upm.edu.my/id/eprint/57482/
_version_ 1643836500832419840
score 13.211869

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