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Combinatorial structure associated with low-dimensional filiform leibniz algebras

This thesis is concerned on the studying a graph representation of (n + 1)- dimensional filiform Leibniz algebras. The filiform Leibniz algebras contain three subclasses called first, second and third class that are denoted in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respec...

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Main Author:	Ahmad Jamri, Ayu Ameliatul Shahilah
Format:	Thesis
Language:	English
Published:	2017
Online Access:	http://psasir.upm.edu.my/id/eprint/69419/1/IPM%202018%202%20IR.pdf http://psasir.upm.edu.my/id/eprint/69419/
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id	my.upm.eprints.69419
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spelling	my.upm.eprints.694192019-07-10T00:57:12Z http://psasir.upm.edu.my/id/eprint/69419/ Combinatorial structure associated with low-dimensional filiform leibniz algebras Ahmad Jamri, Ayu Ameliatul Shahilah This thesis is concerned on the studying a graph representation of (n + 1)- dimensional filiform Leibniz algebras. The filiform Leibniz algebras contain three subclasses called first, second and third class that are denoted in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respectively. This research deals with combinatorial structures associated with FLbn(K) and SLbn(K). Therefore, an algorithm is defined in order to construct such structures associated with filiform Leibniz algebras. By using the table of multiplication of filiform Leibniz algebras, an algorithm for the combinatorial structures associated with filiform Leibniz algebras will be obtained. Next, the structural properties of the combinatorial structure will be constructed to show the non-isomorphism between two classes of filiform Leibniz algebras in such a way of graph theory. Hence, some propositions on combinatorial structures regarding number of vertices and edge, components, degree of vertices, diameter and degree sequences are given. Besides that, an algorithm will be used on association the combinatorial structures with the isomorphism classes of FLbn(K) and SLbn(K). Thus, any two isomorphism classes of FLbn(K) or SLbn(K) are non-isomorphic using combinatorial structures. 2017-04 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/69419/1/IPM%202018%202%20IR.pdf Ahmad Jamri, Ayu Ameliatul Shahilah (2017) Combinatorial structure associated with low-dimensional filiform leibniz algebras. Masters thesis, Universiti Putra Malaysia.
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	This thesis is concerned on the studying a graph representation of (n + 1)- dimensional filiform Leibniz algebras. The filiform Leibniz algebras contain three subclasses called first, second and third class that are denoted in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respectively. This research deals with combinatorial structures associated with FLbn(K) and SLbn(K). Therefore, an algorithm is defined in order to construct such structures associated with filiform Leibniz algebras. By using the table of multiplication of filiform Leibniz algebras, an algorithm for the combinatorial structures associated with filiform Leibniz algebras will be obtained. Next, the structural properties of the combinatorial structure will be constructed to show the non-isomorphism between two classes of filiform Leibniz algebras in such a way of graph theory. Hence, some propositions on combinatorial structures regarding number of vertices and edge, components, degree of vertices, diameter and degree sequences are given. Besides that, an algorithm will be used on association the combinatorial structures with the isomorphism classes of FLbn(K) and SLbn(K). Thus, any two isomorphism classes of FLbn(K) or SLbn(K) are non-isomorphic using combinatorial structures.
format	Thesis
author	Ahmad Jamri, Ayu Ameliatul Shahilah
spellingShingle	Ahmad Jamri, Ayu Ameliatul Shahilah Combinatorial structure associated with low-dimensional filiform leibniz algebras
author_facet	Ahmad Jamri, Ayu Ameliatul Shahilah
author_sort	Ahmad Jamri, Ayu Ameliatul Shahilah
title	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_short	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_full	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_fullStr	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_full_unstemmed	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_sort	combinatorial structure associated with low-dimensional filiform leibniz algebras
publishDate	2017
url	http://psasir.upm.edu.my/id/eprint/69419/1/IPM%202018%202%20IR.pdf http://psasir.upm.edu.my/id/eprint/69419/
_version_	1643839489076887552
score	13.244414

Combinatorial structure associated with low-dimensional filiform leibniz algebras

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