Broadcasts in Graphs: Diametrical Trees
| dc.contributor.author | Gemmrich, L. | |
| dc.contributor.author | Mynhardt, C.M. | |
| dc.date.accessioned | 2017-08-21T19:32:35Z | |
| dc.date.available | 2017-08-21T19:32:35Z | |
| dc.date.copyright | 2017 | en_US |
| dc.date.issued | 2017-08-21 | |
| dc.description | Accepted for publication in the Australasian Journal of Combinatorics | en_US |
| dc.description.abstract | A dominating broadcast on a graph G=(V,E) is a function f:V→{0,1,…,diam(G)} such that f(v)≤e(v) (the eccentricity of v) for all v∈V, and each u∈V is at distance at most f(v) from a vertex v with f(v)≥1. The upper broadcast domination number of G is Γ_{b}(G)=max{∑_{v∈V}f(v):f is a minimal dominating broadcast on G}. As shown by Erwin in [D. Erwin, Cost domination in graphs, Doctoral dissertation, Western Michigan University, 2001], Γ_{b}(G)≥diam(G) for any graph G. We investigate trees whose upper broadcast domination number equal their diameter and, among more general results, characterise caterpillars with this property. | en_US |
| dc.description.reviewstatus | Reviewed | en_US |
| dc.description.scholarlevel | Faculty | en_US |
| dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/8436 | |
| dc.language.iso | en | en_US |
| dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Canada | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ | * |
| dc.subject | broadcast on a graph | en_US |
| dc.subject | dominating broadcast | en_US |
| dc.subject | minimal dominating broadcast | en_US |
| dc.subject | upper broadcast domination number | en_US |
| dc.title | Broadcasts in Graphs: Diametrical Trees | en_US |
| dc.type | Postprint | en_US |