Liar’s dominating sets in graphs

A set L⊆V of a graph G=(V,E) is a liar’s dominating set if (1) for every vertex u∈V, |N[u]∩L|≥2 and (2) for every pair u,v∈V of distinct vertices, |(N[u]∪N[v])∩L|≥3. In this paper, we first provide a characterization of graphs G with γLR(G)=|V| as well as the trees T with γLR(T)=|V|−1. Then we prese...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 211; pp. 204 - 210
Main Authors Alimadadi, Abdollah, Chellali, Mustapha, Mojdeh, Doost Ali
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2016
Subjects
[formula omitted]-partite graph
Double domination
Graph theory
Graphs
Liar’s domination
Mathematical analysis
Packing number
Trees
Upper bounds
Double domination
Liar’s domination
r-partite graph
Packing number
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Summary:A set L⊆V of a graph G=(V,E) is a liar’s dominating set if (1) for every vertex u∈V, |N[u]∩L|≥2 and (2) for every pair u,v∈V of distinct vertices, |(N[u]∪N[v])∩L|≥3. In this paper, we first provide a characterization of graphs G with γLR(G)=|V| as well as the trees T with γLR(T)=|V|−1. Then we present some bounds on the liar’s domination number, especially an upper bound for the ratio between the liar’s domination number and the double domination number is established for connected graphs with girth at least five. Finally, we determine the exact value of the liar’s domination number for the complete r-partite graphs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2016.04.023