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Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology

Graph colouring is the labelling of the elements of a graph subject to certain constraints. It is divided into vertex and edge colouring. In both cases, the assignment of labels, traditionally called colours is such that two vertices or edges must not have the same colour. This has various applicati...

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Main Authors: Chien, Stephen Lim Ern, Raja Maamor Shah, Raja Noor Farah Azura, Othman, Mohamed
Format: Article
Language:English
Published: Penerbit UTM Press 2017
Online Access:http://psasir.upm.edu.my/id/eprint/52398/1/Chromatic%20numbers%20and%20indices%20of%20the%20optimised%20degree%20six%203-modified%20chordal%20ring%20network%20topology.pdf
http://psasir.upm.edu.my/id/eprint/52398/
http://www.mjfas.utm.my/index.php/mjfas/article/view/519
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spelling my.upm.eprints.523982017-06-06T08:28:04Z http://psasir.upm.edu.my/id/eprint/52398/ Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology Chien, Stephen Lim Ern Raja Maamor Shah, Raja Noor Farah Azura Othman, Mohamed Graph colouring is the labelling of the elements of a graph subject to certain constraints. It is divided into vertex and edge colouring. In both cases, the assignment of labels, traditionally called colours is such that two vertices or edges must not have the same colour. This has various applications, especially in parallel computing. This paper introduces the degree six 3-modified chordal ring, CHR6o3, a parallel network interconnection topology model, and discusses its node and link colouring. Despite its asymmetry, the chromatic number of CHR6o3 cannot be generalised and must be determined specifically based on the combination of chords in each case. Cases where the chromatic index of CHR6o3 is its degree and where it is its one colour more than its degree were generalised and proven. Chromatic numbers are important in minimising the completion times of processes in parallel processing by reducing points of synchronisation, and link colouring aids processor scheduling. Penerbit UTM Press 2017 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/52398/1/Chromatic%20numbers%20and%20indices%20of%20the%20optimised%20degree%20six%203-modified%20chordal%20ring%20network%20topology.pdf Chien, Stephen Lim Ern and Raja Maamor Shah, Raja Noor Farah Azura and Othman, Mohamed (2017) Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology. Malaysian Journal of Fundamental and Applied Sciences, 13 (1). pp. 27-30. ISSN 2289-5981; ESSN: 2289-599X http://www.mjfas.utm.my/index.php/mjfas/article/view/519
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 Graph colouring is the labelling of the elements of a graph subject to certain constraints. It is divided into vertex and edge colouring. In both cases, the assignment of labels, traditionally called colours is such that two vertices or edges must not have the same colour. This has various applications, especially in parallel computing. This paper introduces the degree six 3-modified chordal ring, CHR6o3, a parallel network interconnection topology model, and discusses its node and link colouring. Despite its asymmetry, the chromatic number of CHR6o3 cannot be generalised and must be determined specifically based on the combination of chords in each case. Cases where the chromatic index of CHR6o3 is its degree and where it is its one colour more than its degree were generalised and proven. Chromatic numbers are important in minimising the completion times of processes in parallel processing by reducing points of synchronisation, and link colouring aids processor scheduling.
format Article
author Chien, Stephen Lim Ern
Raja Maamor Shah, Raja Noor Farah Azura
Othman, Mohamed
spellingShingle Chien, Stephen Lim Ern
Raja Maamor Shah, Raja Noor Farah Azura
Othman, Mohamed
Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
author_facet Chien, Stephen Lim Ern
Raja Maamor Shah, Raja Noor Farah Azura
Othman, Mohamed
author_sort Chien, Stephen Lim Ern
title Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
title_short Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
title_full Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
title_fullStr Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
title_full_unstemmed Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
title_sort chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology
publisher Penerbit UTM Press
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/52398/1/Chromatic%20numbers%20and%20indices%20of%20the%20optimised%20degree%20six%203-modified%20chordal%20ring%20network%20topology.pdf
http://psasir.upm.edu.my/id/eprint/52398/
http://www.mjfas.utm.my/index.php/mjfas/article/view/519
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score 13.211869

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