Some graphs of metabelian groups of order 24 and their energy

The energy of a graph G is the sum of all absolute values of the eigenvalues of the adjacency matrix. An adjacency matrix is a square matrix where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. A commuting graph of a group is a graph whose verte...

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Main Author:	Ahmad Fadzil, Amira Fadina
Format:	Thesis
Language:	English
Published:	2017
Subjects:	Q Science (General)
Online Access:	http://eprints.utm.my/id/eprint/85758/1/AmiraFadinaAhmadFadzilMFS2017.pdf
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spelling	my-utm-ep.857582020-07-30T07:30:47Z Some graphs of metabelian groups of order 24 and their energy 2017 Ahmad Fadzil, Amira Fadina Q Science (General) The energy of a graph G is the sum of all absolute values of the eigenvalues of the adjacency matrix. An adjacency matrix is a square matrix where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. A commuting graph of a group is a graph whose vertex set is the non-central elements of the group and whose edges are pairs of vertices that commute. Meanwhile, a noncommuting graph is a graph whose vertex set is the non-central elements of the group but the edges are the pairs of vertices that do not commute. A conjugacy class graph is a graph with the non-central conjugacy classes vertices. Two vertices are connected if the order of the conjugacy classes have a common prime divisor. Besides, a conjugate graph is a graph whose vertex set is the non-central elements of the group where two distinct vertices are joined if they are conjugate. Furthermore, a group G is said to be metabelian if there exists a normal subgroup H in G such that both H and the factor group G/H are abelian. In this research, the energies of commuting graphs, noncommuting graphs, conjugacy class graphs and conjugate graphs for all nonabelian metabelian group of order 24 are determined. The computations of the graphs and adjacency matrices for the energy of graphs are determined with the assistance of Groups, Algorithms and Programming (GAP) and Maple 2016 softwares. The results show that the energy of graphs of the groups in the study must be an even integer in the case that the energy is rational. 2017 Thesis http://eprints.utm.my/id/eprint/85758/ http://eprints.utm.my/id/eprint/85758/1/AmiraFadinaAhmadFadzilMFS2017.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:132585 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	Q Science (General)
spellingShingle	Q Science (General) Ahmad Fadzil, Amira Fadina Some graphs of metabelian groups of order 24 and their energy
description	The energy of a graph G is the sum of all absolute values of the eigenvalues of the adjacency matrix. An adjacency matrix is a square matrix where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. A commuting graph of a group is a graph whose vertex set is the non-central elements of the group and whose edges are pairs of vertices that commute. Meanwhile, a noncommuting graph is a graph whose vertex set is the non-central elements of the group but the edges are the pairs of vertices that do not commute. A conjugacy class graph is a graph with the non-central conjugacy classes vertices. Two vertices are connected if the order of the conjugacy classes have a common prime divisor. Besides, a conjugate graph is a graph whose vertex set is the non-central elements of the group where two distinct vertices are joined if they are conjugate. Furthermore, a group G is said to be metabelian if there exists a normal subgroup H in G such that both H and the factor group G/H are abelian. In this research, the energies of commuting graphs, noncommuting graphs, conjugacy class graphs and conjugate graphs for all nonabelian metabelian group of order 24 are determined. The computations of the graphs and adjacency matrices for the energy of graphs are determined with the assistance of Groups, Algorithms and Programming (GAP) and Maple 2016 softwares. The results show that the energy of graphs of the groups in the study must be an even integer in the case that the energy is rational.
format	Thesis
qualification_level	Master's degree
author	Ahmad Fadzil, Amira Fadina
author_facet	Ahmad Fadzil, Amira Fadina
author_sort	Ahmad Fadzil, Amira Fadina
title	Some graphs of metabelian groups of order 24 and their energy
title_short	Some graphs of metabelian groups of order 24 and their energy
title_full	Some graphs of metabelian groups of order 24 and their energy
title_fullStr	Some graphs of metabelian groups of order 24 and their energy
title_full_unstemmed	Some graphs of metabelian groups of order 24 and their energy
title_sort	some graphs of metabelian groups of order 24 and their energy
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/85758/1/AmiraFadinaAhmadFadzilMFS2017.pdf
_version_	1747818449847975936

Some graphs of metabelian groups of order 24 and their energy

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