Domination Number, Independent Domination Number and 2-Independence Number in Trees

Abstract For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees attaining equality. Also we prove that for every tree T of order n ≥ 2, i(T)≤3β2(T)4 i(T) \le {{3{\beta _2}(T)} \over 4} , and we characterize all extreme trees.