Independent transversal total domination versus total domination in trees

Abstract

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 gamma(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 gamma(u) (G). Based on the fact that for any tree T, gamma(t) (T) <= gamma(u) (T) <= gamma(t) (T) + 1, in this work we give several relationship(s) between gamma(u) (T) and gamma(t) (T) for trees T which are leading to classify the trees which are satisfying the equality in these bounds