Hamiltonicity of connected domination critical graphs
© 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connect...
| Main Authors: | , , |
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| Format: | Journal Article |
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Charles Babbage
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/68952 |
| _version_ | 1848761929882927104 |
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| author | Kaemawichanurat, P. Caccetta, Louis Ananchuen, W. |
| author_facet | Kaemawichanurat, P. Caccetta, Louis Ananchuen, W. |
| author_sort | Kaemawichanurat, P. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connected k-yc-critical graphs are Hamiltonian. In this paper, for I > 2, we prove that if k - 1,2 or 3, then every l-connected k-yc-critical graph is Hamiltonian. We further show that, for n > (k - 1)k + 3, the class of i-connected Jt-yc-critical non-Hamiltonian graphs of order n is empty if and only if k = 1,2 or 3. |
| first_indexed | 2025-11-14T10:39:29Z |
| format | Journal Article |
| id | curtin-20.500.11937-68952 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:39:29Z |
| publishDate | 2018 |
| publisher | Charles Babbage |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-689522018-06-29T12:27:52Z Hamiltonicity of connected domination critical graphs Kaemawichanurat, P. Caccetta, Louis Ananchuen, W. © 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connected k-yc-critical graphs are Hamiltonian. In this paper, for I > 2, we prove that if k - 1,2 or 3, then every l-connected k-yc-critical graph is Hamiltonian. We further show that, for n > (k - 1)k + 3, the class of i-connected Jt-yc-critical non-Hamiltonian graphs of order n is empty if and only if k = 1,2 or 3. 2018 Journal Article http://hdl.handle.net/20.500.11937/68952 Charles Babbage restricted |
| spellingShingle | Kaemawichanurat, P. Caccetta, Louis Ananchuen, W. Hamiltonicity of connected domination critical graphs |
| title | Hamiltonicity of connected domination critical graphs |
| title_full | Hamiltonicity of connected domination critical graphs |
| title_fullStr | Hamiltonicity of connected domination critical graphs |
| title_full_unstemmed | Hamiltonicity of connected domination critical graphs |
| title_short | Hamiltonicity of connected domination critical graphs |
| title_sort | hamiltonicity of connected domination critical graphs |
| url | http://hdl.handle.net/20.500.11937/68952 |