Independent Transversal Total Domination versus Total Domination in Trees

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 γ_t(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 γ_tt(G). Based on the fact that for any tree T, γ_t(T) ≤ γ_tt(T) ≤ γ_t(T) + 1, in this work we give several relationships between γ_tt(T) and γ_t(T) for trees T which are leading to classify the trees which are satisfying the equality in these bounds.