Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs
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| Format: | Thesis |
| Language: | English |
| Published: |
2007
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| Online Access: | https://ir.upsi.edu.my/detailsg.php?det=828 |
| Abstract | Abstract here |
| _version_ | 1855625579557027840 |
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| author | Nor Suriya Abd Karim |
| author_facet | Nor Suriya Abd Karim |
| author_sort | Nor Suriya Abd Karim |
| description | |
| format | Thesis |
| id | upsi-828 |
| institution | Universiti Pendidikan Sultan Idris |
| language | English |
| publishDate | 2007 |
| record_format | sWADAH |
| record_pdf | Restricted |
| spelling | upsi-8282020-02-27 Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs 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 N/A openAccess Doctoral Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik N/A |
| spellingShingle | QA Mathematics Nor Suriya Abd Karim Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs |
| thesis_level | PhD |
| title | Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs |
| title_full | Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs |
| title_fullStr | Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs |
| title_full_unstemmed | Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs |
| title_short | Chromaticity of K4-Homeomorphs with Girth 9 and 6-Bridge Graphs |
| title_sort | chromaticity of k4 homeomorphs with girth 9 and 6 bridge graphs |
| topic | QA Mathematics |
| url | https://ir.upsi.edu.my/detailsg.php?det=828 |
| work_keys_str_mv | AT norsuriyaabdkarim chromaticityofk4homeomorphswithgirth9and6bridgegraphs |