Broadcasts in graphs

We say that a function f : V → { 0 , 1 , … , diam ( G ) } is a broadcast if for every vertex v ∈ V , f ( v ) ⩽ e ( v ) , where diam ( G ) denotes the diameter of G and e ( v ) denotes the eccentricity of v . The cost of a broadcast is the value f ( V ) = ∑ v ∈ V f ( v ) . In this paper we introduce...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 154; no. 1; pp. 59 - 75
Main Authors Dunbar, Jean E., Erwin, David J., Haynes, Teresa W., Hedetniemi, Sandra M., Hedetniemi, Stephen T.
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 2006
Amsterdam Elsevier
New York, NY
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Broadcasts
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Designs and configurations
Distance domination
Domination
Exact sciences and technology
Graph theory
Independent sets
Mathematics
Packings
Sciences and techniques of general use
Theoretical computing
Domination
Packings
Distance domination
Independent sets
Broadcasts
Packing
Computer theory
Independent set
Combinatorics
Diffusion
Optimization
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Summary:We say that a function f : V → { 0 , 1 , … , diam ( G ) } is a broadcast if for every vertex v ∈ V , f ( v ) ⩽ e ( v ) , where diam ( G ) denotes the diameter of G and e ( v ) denotes the eccentricity of v . The cost of a broadcast is the value f ( V ) = ∑ v ∈ V f ( v ) . In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs, including dominating, independent and efficient broadcasts.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2005.07.009