ON TREES WITH EQUAL TOTAL DOMINATION AND 2-OUTER-INDEPENDENT DOMINATION NUMBERS

For a graph G = (V, E), a subset D subset of V(G) is a total dominating set if every vertex of G has a neighbor in D. The total domination number of G is the minimum cardinality of a total dominating set of G. A subset D subset of V (G) is a 2-dominating set of G if every vertex of V(G) \ D has at least two neighbors in D, while it is a 2-outer-independent dominating set of G if additionally the set V(G) \ D is independent. The 2-outer-independent domination number of G is the minimum cardinality of a 2-outer-independent dominating set of G. We characterize all trees with equal total domination and 2-outer-independent domination numbers.