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...
| 主要作者: | |
|---|---|
| 格式: | Thesis |
| 出版: |
2010
|
| 主题: |
| _version_ | 1849734253245366272 |
|---|---|
| author | Ong, Poh Hwa |
| author_facet | Ong, Poh Hwa |
| author_sort | Ong, Poh Hwa |
| 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. |
| format | Thesis |
| id | oai:studentsrepo.um.edu.my:6094 |
| institution | Universiti Malaya |
| publishDate | 2010 |
| record_format | eprints |
| spelling | oai:studentsrepo.um.edu.my: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-record | http://studentsrepo.um.edu.my/6094/ |
| work_keys_str_mv | AT ongpohhwa onselfcliquegraphsongpohhwa |