Discussiones Mathematicae Graph Theory 30(2) (2010)
223-235
DOI: https://doi.org/10.7151/dmgt.1488
ON LOCATING-DOMINATION IN GRAPHS
Mustapha Chellali, Malika Mimouni
LAMDA-RO Laboratory |
Peter J. Slater
Department of Mathematics and Computer Science Department |
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 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
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