Domination, independent domination number and 2-independence number in trees
Hamideh Aram, Nasrin Dehgardi, Seyed Mahmoud Sheikholeslami, Mina Valinavaz, Lutz Volkmann · Discussiones Mathematicae Graph Theory · 2018
For a graph G, let (G) be the domination number, i(G) be the independent domination number and 2 (G) be the 2-independence number. In this paper, we prove that for any tree T of order n 2, 4 2 (T ) -3(T ) 3i(T ), and we characterize all trees attaining equality. Also we prove that for every tree T of order n 2, i(T ) 32(T ) 4 , and we characterize all extreme trees.