Geodesic
A characterization of locating-total domination edge critical graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 1, pp. 197-202.

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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, N_G(u) ∩ D ≠ N_G(v) ∩ D. The locating-total domination number γ_L^t(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 γ_L^t+-ER-critical graph, if γ_L^t(G-e) > γ_L^t(G) for all e non-pendant edge of E. The purpose of this paper is to characterize the class of γ_L^t+-ER-critical graphs.
Keywords: locating-domination, critical graph 
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Blidia, Mostafa; Dali, Widad. A characterization of locating-total domination edge critical graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 1, pp. 197-202. http://geodesic.mathdoc.fr/item/DMGT_2011_31_1_a12/

[1] M. Blidia and W. Dali, A characterization of a locating-domination edge critical graphs, Australasian J. Combin. 44 (2009) 297-300.

[2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).

[3] D.P. Sumner and P. Blitch, Domination critical graphs, J. Combin. Theory (B) 34 (1983) 65-76, doi: 10.1016/0095-8956(83)90007-2.

[4] T.W. Haynes, M.A. Henning and J. Howard, Locating and total dominating sets in trees, Discrete Appl. Math. 154 (2006) 1293-1300, doi: 10.1016/j.dam.2006.01.002.