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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
http://psasir.upm.edu.my/id/eprint/9335/
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spelling my.upm.eprints.93352024-02-20T03:36:37Z http://psasir.upm.edu.my/id/eprint/9335/ Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs 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. 2001-03 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf Omoomi, Behnaz (2001) Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs. Doctoral thesis, Universiti Putra Malaysia. Chromatographic analysis English
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
English
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
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
publishDate 2001
url http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf
http://psasir.upm.edu.my/id/eprint/9335/
_version_ 1792154417690050560
score 13.211869

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