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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| Format: | Thesis |
| Language: | English English |
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2001
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| Online Access: | http://psasir.upm.edu.my/id/eprint/9335/ http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf |
| _version_ | 1848841117908336640 |
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| author | Omoomi, Behnaz |
| author_facet | Omoomi, Behnaz |
| author_sort | Omoomi, Behnaz |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T07:38:09Z |
| format | Thesis |
| id | upm-9335 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:38:09Z |
| publishDate | 2001 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| spellingShingle | Chromatographic analysis Omoomi, Behnaz Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs |
| title | 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_short | Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs |
| title_sort | chromatic equivalence classes and chromatic defining numbers of certain graphs |
| topic | Chromatographic analysis |
| url | http://psasir.upm.edu.my/id/eprint/9335/ http://psasir.upm.edu.my/id/eprint/9335/1/FSAS_2001_57.pdf |