Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs

There are two parts in this dissertation: the chromatic equivalence classes and the chromatic defining numbers of graphs. In the first part the chromaticity of the family of generalized polygon trees with intercourse number two, denoted by Cr (a, b; c, d), is studied. It is known that Cr( a, b;...

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Main Author:	Omoomi, Behnaz
Format:	Thesis
Language:	English English
Published:	2001
Subjects:	Chromatographic analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf
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id	my-upm-ir.9335
record_format	uketd_dc
spelling	my-upm-ir.93352024-02-20T03:36:37Z Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs 2001-03 Omoomi, Behnaz There are two parts in this dissertation: the chromatic equivalence classes and the chromatic defining numbers of graphs. In the first part the chromaticity of the family of generalized polygon trees with intercourse number two, denoted by Cr (a, b; c, d), is studied. It is known that Cr( a, b; c, d) is a chromatic equivalence class if min {a, b, c, d} ≥ r+3. We consider Cr( a, b; c, d) when min{ a, b, c, d} ≤ r + 2. The necessary and sufficient conditions for Cr(a, b; c, d) with min {a, b, c, d} ≤ r + 2 to be a chromatic equivalence class are given. Thus, the chromaticity of Cr (a, b; c, d) is completely characterized. In the second part the defining numbers of regular graphs are studied. Let d(n, r, X = k) be the smallest value of defining numbers of all r-regular graphs of order n and the chromatic number equals to k. It is proved that for a given integer k and each r ≥ 2(k - 1) and n ≥ 2k, d(n, r, X = k) = k - 1. Next, a new lower bound for the defining numbers of r-regular k-chromatic graphs with k < r < 2( k - 1) is found. Finally, the value of d( n , r, X = k) when k < r < 2(k - 1) for certain values of n and r is determined. Chromatographic analysis 2001-03 Thesis http://psasir.upm.edu.my/id/eprint/9335/ http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf text en public doctoral Universiti Putra Malaysia Chromatographic analysis Faculty of Science and Environmental Studies Peng, Vee Hock English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
advisor	Peng, Vee Hock
topic	Chromatographic analysis
spellingShingle	Chromatographic analysis Omoomi, Behnaz Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
description	There are two parts in this dissertation: the chromatic equivalence classes and the chromatic defining numbers of graphs. In the first part the chromaticity of the family of generalized polygon trees with intercourse number two, denoted by Cr (a, b; c, d), is studied. It is known that Cr( a, b; c, d) is a chromatic equivalence class if min {a, b, c, d} ≥ r+3. We consider Cr( a, b; c, d) when min{ a, b, c, d} ≤ r + 2. The necessary and sufficient conditions for Cr(a, b; c, d) with min {a, b, c, d} ≤ r + 2 to be a chromatic equivalence class are given. Thus, the chromaticity of Cr (a, b; c, d) is completely characterized. In the second part the defining numbers of regular graphs are studied. Let d(n, r, X = k) be the smallest value of defining numbers of all r-regular graphs of order n and the chromatic number equals to k. It is proved that for a given integer k and each r ≥ 2(k - 1) and n ≥ 2k, d(n, r, X = k) = k - 1. Next, a new lower bound for the defining numbers of r-regular k-chromatic graphs with k < r < 2( k - 1) is found. Finally, the value of d( n , r, X = k) when k < r < 2(k - 1) for certain values of n and r is determined.
format	Thesis
qualification_level	Doctorate
author	Omoomi, Behnaz
author_facet	Omoomi, Behnaz
author_sort	Omoomi, Behnaz
title	Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
title_short	Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
title_full	Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
title_fullStr	Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
title_full_unstemmed	Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
title_sort	chromatic equivalence classes and chromatic defining numbers of certain graphs
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science and Environmental Studies
publishDate	2001
url	http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf
_version_	1794018824053325824

Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs

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