Authors:
H. Aram, N. Dehgardi, S.M. Sheikholeslami, M. Valinavaz, L. Volkmann
Title:
Domination, independent domination number and 2-independence number in trees
Source:
Discussiones Mathematicae Graph Theory
Received 04.07.2017, Revised 07.07.2018, Accepted 09.07.2018, doi: 10.7151/dmgt.2165

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, 2(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)\le \frac{3β2(T)}{4}, and we characterize all extreme trees.
Keywords:
2-independence number, domination number, independent domination number

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