Geodesic
Independent Transversal Total Domination versus Total Domination in Trees
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 213-224

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A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G). A total dominating set of G having nonempty intersection with all the independent sets of maximum cardinality in G is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by γtt(G). Based on the fact that for any tree T, γt(T) ≤ γtt(T) ≤ γt(T) + 1, in this work we give several relationships between γtt(T) and γt(T) for trees T which are leading to classify the trees which are satisfying the equality in these bounds.
Keywords: independent transversal total domination number, total domination number, independence number, trees 
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Martínez, Abel Cabrera; Peterin, Iztok; Yero, Ismael G. Independent Transversal Total Domination versus Total Domination in Trees. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 213-224. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a13/