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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主要作者: Ong, Poh Hwa
格式: Thesis
出版: 2010
主题:
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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.
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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