Trees with equal broadcast and domination numbers
| dc.contributor.author | Lunney, Scott | |
| dc.contributor.supervisor | Mynhardt, C. M. | |
| dc.date.accessioned | 2011-12-19T23:18:14Z | |
| dc.date.available | 2011-12-19T23:18:14Z | |
| dc.date.copyright | 2011 | en_US |
| dc.date.issued | 2011-12-19 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | A broadcast on a graph G=(V,E) is a function f : V → {0, ..., diam(G)} that assigns an integer value to each vertex such that, for each v ∈ V , f (v) ≤ e(v), the eccentricity of v. The broadcast number of a graph is the minimum value of Σv∈V f (v) among all broadcasts f with the property that for each vertex x of V, f (v) ≥ d(x, v) for some vertex v having positive f (v). This number is bounded above by both the radius of the graph and its domination number. Graphs for which the broadcast number is equal to the domination number are called 1-cap graphs. We investigate and characterize a class of 1-cap trees. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/3746 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | Broadcasts in Graphs | en_US |
| dc.subject | Dominating Broadcasts | en_US |
| dc.title | Trees with equal broadcast and domination numbers | en_US |
| dc.type | Thesis | en_US |