Discussiones Mathematicae Graph Theory 30(2) (2010) 223-235
doi: 10.7151/dmgt.1488

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Mustapha Chellali,  Malika Mimouni

LAMDA-RO Laboratory
Department of Mathematics, University of Blida
B.P. 270, Blida, Algeria
e-mail: m_chellali@yahoo.com

Peter J. Slater

Department of Mathematics and Computer Science Department
University of Alabama in Huntsville
Huntsville, AL 35899 USA
e-mail: slaterp@email.uah.edu


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 γL(G) is the minimum cardinality of a LDS of G, and the upper locating-domination number, ΓL(G) is the maximum cardinality of a minimal LDS of G. We present different bounds on ΓL(G) and γL(G).

Keywords: upper locating-domination number, locating-domination number.

2010 Mathematics Subject Classification: 05C69.


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Received 16 December 2008
Revised 8 June 2009
Accepted 8 June 2009