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
Sub-type Article (original research)
DOI 10.1016/j.disc.2009.04.024
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
 
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Created: Thu, 28 Jan 2016, 11:37:37 EST by Kay Mackie on behalf of School of Mathematics & Physics