Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group

A Cayley graph is a structure consisting of vertices and edges that describes the information of a group and its generators where two vertices are connected by a directed edge in certain conditions. This research focuses on the prime order and composite order Cayley graphs on the generalised quatern...

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Main Author:	Muhidin, Omarfaidullah Pahil
Format:	Thesis
Language:	English
Published:	2020
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/101619/1/OmarfaidullahPahilMuhidinMFS2020.pdf
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id	my-utm-ep.101619
record_format	uketd_dc
spelling	my-utm-ep.1016192023-07-03T02:53:51Z Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group 2020 Muhidin, Omarfaidullah Pahil QA Mathematics A Cayley graph is a structure consisting of vertices and edges that describes the information of a group and its generators where two vertices are connected by a directed edge in certain conditions. This research focuses on the prime order and composite order Cayley graphs on the generalised quaternion group and the quasidihedral group, where the subsets are the set of prime order and composite order element of each group. The properties of elements of both groups are investigated, and then the structures of prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group are obtained. Besides, the properties of the graph such as chromatic number, independence number, clique number, diameter, girth, and graph planarity are found. From this research, it is shown that the prime order and composite order Cayley graphs of both generalised quaternion group and quasi-dihedral group consist of unions of isomorphic components of equal vertices and a regular connected graph, respectively. 2020 Thesis http://eprints.utm.my/id/eprint/101619/ http://eprints.utm.my/id/eprint/101619/1/OmarfaidullahPahilMuhidinMFS2020.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146340 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Muhidin, Omarfaidullah Pahil Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group
description	A Cayley graph is a structure consisting of vertices and edges that describes the information of a group and its generators where two vertices are connected by a directed edge in certain conditions. This research focuses on the prime order and composite order Cayley graphs on the generalised quaternion group and the quasidihedral group, where the subsets are the set of prime order and composite order element of each group. The properties of elements of both groups are investigated, and then the structures of prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group are obtained. Besides, the properties of the graph such as chromatic number, independence number, clique number, diameter, girth, and graph planarity are found. From this research, it is shown that the prime order and composite order Cayley graphs of both generalised quaternion group and quasi-dihedral group consist of unions of isomorphic components of equal vertices and a regular connected graph, respectively.
format	Thesis
qualification_level	Master's degree
author	Muhidin, Omarfaidullah Pahil
author_facet	Muhidin, Omarfaidullah Pahil
author_sort	Muhidin, Omarfaidullah Pahil
title	Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group
title_short	Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group
title_full	Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group
title_fullStr	Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group
title_full_unstemmed	Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group
title_sort	prime order and composite order cayley graphs of generalised quaternion group and quasi-dihedral group
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2020
url	http://eprints.utm.my/id/eprint/101619/1/OmarfaidullahPahilMuhidinMFS2020.pdf
_version_	1776100739795386368

Prime order and composite order Cayley graphs of generalised quaternion group and quasi-dihedral group

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