Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)

The chromaticity of graphs is the term used referring to the question of chromatic equivalence and chromatic uniqueness of graphs. Since the arousal of the interest on the chromatically equivalent and chromatically unique graphs, various concepts and results under the said areas of research have bee...

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Main Author:	Nor Suriya Abd Karim
Format:	thesis
Language:	eng
Published:	2007
Subjects:	QA Mathematics
Online Access:	https://ir.upsi.edu.my/detailsg.php?det=828
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spelling	oai:ir.upsi.edu.my:8282020-02-27 Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR) 2007 Nor Suriya Abd Karim QA Mathematics The chromaticity of graphs is the term used referring to the question of chromatic equivalence and chromatic uniqueness of graphs. Since the arousal of the interest on the chromatically equivalent and chromatically unique graphs, various concepts and results under the said areas of research have been discovered and many families of such graphs have been obtained. The purpose of this thesis is to contribute new results on the chromaticity of graphs, specifically, K4 - homeomorphs with girth 9 and 6-bridge graphs. A K4 - homeomorph is a graph derived from a complete graph, K4. Such a homeomorph is denoted by K4(a, b, c, d, e, f) where the six edges of K4 are replaced by the six paths of length a, b, c, d, e and f. Let N and Ok be a set of natural numbers and a multigraph with two vertices and k edges, respectively. For any aI, a2, ... , ak E N, the graph O(al' a2, ... , ak) is a subdivision ofOk where the edged of Ok are replaced by paths of length a1,a2,...,ak,respectively. The subdivision of Ok is called a multi-bridge graph or a k-bridge graph. The results in this thesis cover two main parts. The first part involves the chromaticity of K4 - homeomorphs with girth 9 and the second part discusses the chromaticity of 6-bridge graphs. We first study the chromaticity of a type of K4-homeomorphs with girth 9, that is, the graph K4(2,3,4,d,e,f). We then investigate the chromaticity of another type of K4-homeomorphs with girth 9, that is, the graph K4(,4,4,d,e,f). Then, we obtain the complete solution for the chromaticity of all types of K4- homeomorphs with girth 9. For the latter part, we first investigate the chromaticity of 6-bridge graph O(3,3,3,b,b,c) where 3<b <c. We next study the chromaticity of 6 bridge graph O(a,a,a,b,b,c) where 2 <a <b <c. We continue to determine the chromaticity of 6-bridge graph O(a,a,b,b,b,c) where 2 2007 thesis https://ir.upsi.edu.my/detailsg.php?det=828 https://ir.upsi.edu.my/detailsg.php?det=828 text eng closedAccess Doctoral Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik N/A
institution	Universiti Pendidikan Sultan Idris
collection	UPSI Digital Repository
language	eng
topic	QA Mathematics
spellingShingle	QA Mathematics Nor Suriya Abd Karim Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)
description	The chromaticity of graphs is the term used referring to the question of chromatic equivalence and chromatic uniqueness of graphs. Since the arousal of the interest on the chromatically equivalent and chromatically unique graphs, various concepts and results under the said areas of research have been discovered and many families of such graphs have been obtained. The purpose of this thesis is to contribute new results on the chromaticity of graphs, specifically, K4 - homeomorphs with girth 9 and 6-bridge graphs. A K4 - homeomorph is a graph derived from a complete graph, K4. Such a homeomorph is denoted by K4(a, b, c, d, e, f) where the six edges of K4 are replaced by the six paths of length a, b, c, d, e and f. Let N and Ok be a set of natural numbers and a multigraph with two vertices and k edges, respectively. For any aI, a2, ... , ak E N, the graph O(al' a2, ... , ak) is a subdivision ofOk where the edged of Ok are replaced by paths of length a1,a2,...,ak,respectively. The subdivision of Ok is called a multi-bridge graph or a k-bridge graph. The results in this thesis cover two main parts. The first part involves the chromaticity of K4 - homeomorphs with girth 9 and the second part discusses the chromaticity of 6-bridge graphs. We first study the chromaticity of a type of K4-homeomorphs with girth 9, that is, the graph K4(2,3,4,d,e,f). We then investigate the chromaticity of another type of K4-homeomorphs with girth 9, that is, the graph K4(,4,4,d,e,f). Then, we obtain the complete solution for the chromaticity of all types of K4- homeomorphs with girth 9. For the latter part, we first investigate the chromaticity of 6-bridge graph O(3,3,3,b,b,c) where 3<b <c. We next study the chromaticity of 6 bridge graph O(a,a,a,b,b,c) where 2 <a <b <c. We continue to determine the chromaticity of 6-bridge graph O(a,a,b,b,b,c) where 2
format	thesis
qualification_name
qualification_level	Doctorate
author	Nor Suriya Abd Karim
author_facet	Nor Suriya Abd Karim
author_sort	Nor Suriya Abd Karim
title	Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)
title_short	Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)
title_full	Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)
title_fullStr	Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)
title_full_unstemmed	Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)
title_sort	chromaticity of k4-homeomorphs with girth 9 and 6-bridge graphs (ir)
granting_institution	Universiti Pendidikan Sultan Idris
granting_department	Fakulti Sains dan Matematik
publishDate	2007
url	https://ir.upsi.edu.my/detailsg.php?det=828
_version_	1747832915614498816

Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs (IR)

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