Geodesic
Bounding the Locating-Total Domination Number of a Tree in Terms of Its Annihilation Number
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 31-40

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Suppose G = (V,E) is a graph with no isolated vertex. A subset S of V is called a locating-total dominating set of G if every vertex in V is adjacent to a vertex in S, and for every pair of distinct vertices u and v in V − S, we have N(u) ∩ S N(v) ∩ S. The locating-total domination number of G, denoted by γ_t^L (G), is the minimum cardinality of a locating-total dominating set of G. The annihilation number of G, denoted by a(G), is the largest integer k such that the sum of the first k terms of the nondecreasing degree sequence of G is at most the number of edges in G. In this paper, we show that for any tree of order n ≥ 2, γ_t^L (T) ≤ a(T) + 1 and we characterize the trees achieving this bound.
Keywords: total domination, locating-total domination, annihilation num- ber, tree 
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Ning, Wenjie; Lu, Mei; Wang, Kun. Bounding the Locating-Total Domination Number of a Tree in Terms of Its Annihilation Number. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 31-40. http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a3/