On self-clique graphs / Ong Poh Hwa
The clique graph of a graph G is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph G is self-clique if it is isomorphic to its clique graph. Clique graphs have been studied for some t...
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| Format: | Thesis |
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2010
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| Online Access: | http://studentsrepo.um.edu.my/6094/ http://studentsrepo.um.edu.my/6094/1/thesis_1.pdf |
| _version_ | 1848773070295138304 |
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| author | Ong, Poh Hwa |
| author_facet | Ong, Poh Hwa |
| author_sort | Ong, Poh Hwa |
| building | UM Research Repository |
| collection | Online Access |
| description | The clique graph of a graph G is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph G is self-clique if it is isomorphic to its clique graph. Clique graphs have been studied for some time. However, not much is known about self-clique graphs. Self-clique graphs were ¯rst introduced
and studied by Escalante [Abh. Math. Sem. Univ. Hamburg 39 (1973) 59-68]. Since then, self-clique graphs have been characterized for some classes of graphs. Chia [Discrete Math. 212 (2000) 185-189] gave a characterization of connected self-clique graphs in which all cliques have size two, except for precisely one clique. The main objective in this thesis is to characterize all connected self-clique
graphs with given clique sizes. Some known results on the characterizations of clique graphs and self-clique graphs are presented. We obtain a characterization for the set of all connected self-clique graphs having all cliques but two of size 2. We also give several results on connected self-clique graphs in which each clique has the same size k for k = 2 and k = 3. |
| first_indexed | 2025-11-14T13:36:33Z |
| format | Thesis |
| id | um-6094 |
| institution | University Malaya |
| institution_category | Local University |
| last_indexed | 2025-11-14T13:36:33Z |
| publishDate | 2010 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | um-60942015-12-02T05:16:41Z On self-clique graphs / Ong Poh Hwa Ong, Poh Hwa Q Science (General) QA Mathematics The clique graph of a graph G is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph G is self-clique if it is isomorphic to its clique graph. Clique graphs have been studied for some time. However, not much is known about self-clique graphs. Self-clique graphs were ¯rst introduced and studied by Escalante [Abh. Math. Sem. Univ. Hamburg 39 (1973) 59-68]. Since then, self-clique graphs have been characterized for some classes of graphs. Chia [Discrete Math. 212 (2000) 185-189] gave a characterization of connected self-clique graphs in which all cliques have size two, except for precisely one clique. The main objective in this thesis is to characterize all connected self-clique graphs with given clique sizes. Some known results on the characterizations of clique graphs and self-clique graphs are presented. We obtain a characterization for the set of all connected self-clique graphs having all cliques but two of size 2. We also give several results on connected self-clique graphs in which each clique has the same size k for k = 2 and k = 3. 2010 Thesis NonPeerReviewed application/pdf http://studentsrepo.um.edu.my/6094/1/thesis_1.pdf Ong, Poh Hwa (2010) On self-clique graphs / Ong Poh Hwa. PhD thesis, University of Malaya. http://studentsrepo.um.edu.my/6094/ |
| spellingShingle | Q Science (General) QA Mathematics Ong, Poh Hwa On self-clique graphs / Ong Poh Hwa |
| title | On self-clique graphs / Ong Poh Hwa |
| title_full | On self-clique graphs / Ong Poh Hwa |
| title_fullStr | On self-clique graphs / Ong Poh Hwa |
| title_full_unstemmed | On self-clique graphs / Ong Poh Hwa |
| title_short | On self-clique graphs / Ong Poh Hwa |
| title_sort | on self-clique graphs / ong poh hwa |
| topic | Q Science (General) QA Mathematics |
| url | http://studentsrepo.um.edu.my/6094/ http://studentsrepo.um.edu.my/6094/1/thesis_1.pdf |