Independent transversal total domination versus total domination in trees
Abel Cabrera Martínez, Iztok Peterin, Ismael G. Yero · Discussiones Mathematicae Graph Theory · 2019
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 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 tt (G). Based on the fact that for any tree T , t (T ) tt (T ) t (T ) + 1, in this work we give several relationships between tt (T ) and t (T ) for trees T which are leading to classify the trees which are satisfying the equality in these bounds.