Discussiones Mathematicae Graph Theory 31(1) (2011)
A CHARACTERIZATION OF LOCATING-TOTAL DOMINATION EDGE CRITICAL GRAPHS
| Mostafa Blidia
LAMDA-RO, Department of Mathematics
University of Blida, B.P. 270, Blida, Algeria
University of Algiers, Algeria
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
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