Radial trees

Herke, S. and Mynhardt, C. M. (2009) Radial trees. Discrete Mathematics, 309 20: 5950-5962. doi:10.1016/j.disc.2009.04.024


Author Herke, S.
Mynhardt, C. M.
Title Radial trees
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
1872-681X
Publication date 2009-10-01
Sub-type Article (original research)
DOI 10.1016/j.disc.2009.04.024
Open Access Status Not Open Access
Volume 309
Issue 20
Start page 5950
End page 5962
Total pages 13
Place of publication Amsterdam, Netherlands
Publisher Elsevier BV
Language eng
Formatted abstract
A broadcast on a graph G is a function f : V → {0, ..., diam G} such that for each v ∈ V, f (v) ≤ e (v) (the eccentricity of v). The broadcast number of G is the minimum value of ∑v ∈ V f (v) among all broadcasts f for which each vertex of G is within distance f (v) from some vertex v having f (v) ≥ 1. This number is bounded above by the radius of G as well as by its domination number. Graphs for which the broadcast number is equal to the radius are called radial; the problem of characterizing radial trees was first discussed in [J. Dunbar, D. Erwin, T. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, Broadcasts in graphs, Discrete Appl. Math. (154) (2006) 59-75]. We provide a characterization of radial trees as well as a geometrical interpretation of our characterization. 
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 9 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 10 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Thu, 28 Jan 2016, 21:37:37 EST by Kay Mackie on behalf of School of Mathematics & Physics