On locating-domination in graphs

Mustapha Chellali; Malika Mimouni; Peter J. Slater

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 2, page 223-235
  • ISSN: 2083-5892

Abstract

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A set D of vertices in a graph G = (V,E) is a locating-dominating set (LDS) if for every two vertices u,v of V-D the sets N(u)∩ D and N(v)∩ D are non-empty and different. The locating-domination number γ L ( G ) is the minimum cardinality of a LDS of G, and the upper locating-domination number, Γ L ( G ) is the maximum cardinality of a minimal LDS of G. We present different bounds on Γ L ( G ) and γ L ( G ) .

How to cite

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Mustapha Chellali, Malika Mimouni, and Peter J. Slater. "On locating-domination in graphs." Discussiones Mathematicae Graph Theory 30.2 (2010): 223-235. <http://eudml.org/doc/270845>.

@article{MustaphaChellali2010,
abstract = {A set D of vertices in a graph G = (V,E) is a locating-dominating set (LDS) if for every two vertices u,v of V-D the sets N(u)∩ D and N(v)∩ D are non-empty and different. The locating-domination number $γ_L(G)$ is the minimum cardinality of a LDS of G, and the upper locating-domination number, $Γ_L(G)$ is the maximum cardinality of a minimal LDS of G. We present different bounds on $Γ_L(G)$ and $γ_L(G)$.},
author = {Mustapha Chellali, Malika Mimouni, Peter J. Slater},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {upper locating-domination number; locating-domination number},
language = {eng},
number = {2},
pages = {223-235},
title = {On locating-domination in graphs},
url = {http://eudml.org/doc/270845},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Mustapha Chellali
AU - Malika Mimouni
AU - Peter J. Slater
TI - On locating-domination in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 2
SP - 223
EP - 235
AB - A set D of vertices in a graph G = (V,E) is a locating-dominating set (LDS) if for every two vertices u,v of V-D the sets N(u)∩ D and N(v)∩ D are non-empty and different. The locating-domination number $γ_L(G)$ is the minimum cardinality of a LDS of G, and the upper locating-domination number, $Γ_L(G)$ is the maximum cardinality of a minimal LDS of G. We present different bounds on $Γ_L(G)$ and $γ_L(G)$.
LA - eng
KW - upper locating-domination number; locating-domination number
UR - http://eudml.org/doc/270845
ER -

References

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