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/

[1] C. Brause, M.A. Henning and M. Krzywkowski, A characterization of trees with equal 2-domination and 2-independence numbers, Discrete Math. Theor. Comput. Sci. 19 (2017) #1. doi: 10.23638/DMTCS-19-1-1

[2] A. Cabrera Martínez, J.M. Sigarreta Almira and I.G. Yero, On the independence transversal total domination number of graphs, Discrete Appl. Math. 219 (2017) 65–73. doi: 10.1016/j.dam.2016.10.033

[3] M. Chellali and T.W. Haynes, A note on the total domination of a tree, J. Combin. Math. Combin. Comput. 58 (2006) 189–193.

[4] M.A. Henning, A survey of selected recent results on total domination in graphs, Discrete Math. 309 (2009) 32–63. doi: 10.1016/j.disc.2007.12.044

[5] M.A. Henning and S.A. Marcon, A constructive characterization of trees with equal total domination and disjunctive domination numbers, Quaest. Math. 39 (2016) 531–543. doi: 10.2989/16073606.2015.1096860

[6] M.A. Henning and A. Yeo, Total Domination in Graphs (Springer, New York, 2013). doi: 10.1007/978-1-4614-6525-6

[7] Z. Li and J. Xu, A characterization of trees with equal independent domination and secure domination numbers, Inform. Process. Lett. 119 (2017) 14–18. doi: 10.1016/j.ipl.2016.11.004