Generalisations of irredundance in graphs
| dc.contributor.author | Finbow, Stephen | |
| dc.contributor.supervisor | Cockayne, E.J. | |
| dc.contributor.supervisor | MacGillivray, Gary | |
| dc.date.accessioned | 2017-04-13T17:55:47Z | |
| dc.date.available | 2017-04-13T17:55:47Z | |
| dc.date.copyright | 2003 | en_US |
| dc.date.issued | 2017-04-13 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Doctor of Philosophy Ph.D. | en_US |
| dc.description.abstract | The well studied class of irredundant vertex sets of a graph has been previously shown to be a special case of (a) a “Private Neighbor Cube” of eight classes of vertex subsets and (b) a family of sixty four classes of “generalised irredundant sets.” The thesis makes various advances in the theory of irredundance. More specifically: (i) Nordhaus-Gaddum results for all the sixty-four classes of generalised irredundant sets are obtained. (ii) Sharp lower bounds involving order and maximum degree are attained for two specific classes in the Private Neighbor Cube. (iii) A new framework which includes both of the above generalisations and various concepts of domination, is proposed. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/7913 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | Graph theory | en_US |
| dc.subject | Domination (Graph theory) | en_US |
| dc.title | Generalisations of irredundance in graphs | en_US |
| dc.type | Thesis | en_US |