Discussiones Mathematicae Graph Theory 31(1) (2011) 197-202
doi: 10.7151/dmgt.1538

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Mostafa Blidia

LAMDA-RO, Department of Mathematics
University of Blida, B.P. 270, Blida, Algeria
e-mail: m_blidia@yahoo.fr.

Widad Dali

Department R-O
University of Algiers, Algeria
e-mail: widdal@yahoo.fr.


For a graph G = (V,E) without isolated vertices, a subset D of vertices of V is a total dominating set (TDS) of G if every vertex in V is adjacent to a vertex in D. The total domination number γt(G) is the minimum cardinality of a TDS of G. A subset D of V which is a total dominating set, is a locating-total dominating set, or just a LTDS of G, if for any two distinct vertices u and v of V(G)∖D, NG(u)∩D ≠ NG(v)∩D. The locating-total domination number γLt(G) is the minimum cardinality of a locating-total dominating set of G. A graph G is said to be a locating-total domination edge removal critical graph, or just a γLt+-ER-critical graph, if γLt(G−e) > γLt(G) for all e non-pendant edge of E. The purpose of this paper is to characterize the class of γLt+-ER-critical graphs.

Keywords: locating-domination, critical graph.

2010 Mathematics Subject Classification: 05C69, 05C15.


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Received 8 December 2008
Revised 20 December 2009
Accepted 21 January 2010