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. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/7913 |
| Date | 13 April 2017 |
| Creators | Finbow, Stephen |
| Contributors | Cockayne, E.J., MacGillivray, Gary |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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