Eternal Domination Problems
| dc.contributor.author | Williams, Ethan | |
| dc.contributor.supervisor | MacGillivray, Gary | |
| dc.contributor.supervisor | Brewster, Richard | |
| dc.date.accessioned | 2023-12-20T01:26:06Z | |
| dc.date.available | 2023-12-20T01:26:06Z | |
| dc.date.copyright | 2023 | en_US |
| dc.date.issued | 2023-12-19 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | Consider placing mobile guards on the vertices of a graph. The vertices are then attacked by an assailant, requiring you to move guards to the attacked vertices. What is the minimum number of guards you need in order to be able to defend against any sequence of attacks? This question is the basis for the eternal domination problem. In this thesis we investigate this problem and introduce new parameters related to it. These new parameters arise from changing three of the assumptions made when defining the game. Specifically we assume that any number of guards can move when defending against an attack; only one attack needs to be defended against at a time; and that any number of guards can occupy a vertex. Changing these assumptions gives rise to the maneuver, invasion, and stacking numbers respectively. We investigate these parameters throughout this thesis, especially as they relate to trees. Additionally, we tackle the related problem of eternal Roman domination, which is based on the topic which originally gave rise to the eternal domination problem. We establish a best possible upper bound for this parameter over all graphs. Finally, we present exponential time algorithms for solving all of these problems, as well as a host of other related problems. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/15735 | |
| 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 | Eternal Domination | en_US |
| dc.title | Eternal Domination Problems | en_US |
| dc.type | Thesis | en_US |