Dominating broadcasts in graphs
| dc.contributor.author | Herke, Sarada Rachelle Anne | |
| dc.contributor.supervisor | Mynhardt, C. M. | |
| dc.date.accessioned | 2009-07-29T21:22:03Z | |
| dc.date.available | 2009-07-29T21:22:03Z | |
| dc.date.copyright | 2009 | en |
| dc.date.issued | 2009-07-29T21:22:03Z | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en |
| dc.description.abstract | A broadcast is a function $f:V \rightarrow { 0,...,diam(G)}$ that assigns an integer value to each vertex such that, for each $v\in V$, $f(v)\leq e(v)$, the eccentricity of $v$. The broadcast number of a graph is the minimum value of $\sum_{v\in V}f(v)$ among all broadcasts $f$ for which each vertex of the graph is within distance $f(v)$ from some vertex $v$ having $f(v)\geq1$. This number is bounded above by the radius of the graph, as well as by its domination number. Graphs for which the broadcast number is equal to the radius are called radial. We prove a new upper bound on the broadcast number of a graph and motivate the study of radial trees by proving a relationship between the broadcast number of a graph and those of its spanning subtrees. We describe some classes of radial trees and then provide a characterization of radial trees, as well as a geometric interpretation of our characterization. | en |
| dc.identifier.bibliographicCitation | S. Herke, C.M. Mynhardt, Radial Trees, Discrete Mathematics (2009), doi:10.1016/j.disc.2009.04.024 | en |
| dc.identifier.uri | http://hdl.handle.net/1828/1479 | |
| dc.language | English | eng |
| dc.language.iso | en | en |
| dc.rights | Available to the World Wide Web | en |
| dc.subject | broadcast | en |
| dc.subject | broadcast domination | en |
| dc.subject | radial tree | en |
| dc.subject | dominating broadcast | en |
| dc.subject.lcsh | UVic Subject Index::Sciences and Engineering::Mathematics::Pure mathematics | en |
| dc.title | Dominating broadcasts in graphs | en |
| dc.type | Thesis | en |