# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

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: 2017-07-04, Revised: 2018-07-07, Accepted: 2018-07-09, https://doi.org/10.7151/dmgt.2165

Abstract:

For a graph $G$, let $\gamma(G)$ be the domination number, $i(G)$ be the independent domination number and $\beta_2(G)$ be the 2-independence number. In this paper, we prove that for any tree $T$ of order $n\ge 2$, $4\beta_{2}(T)-3\gamma(T)\ge 3i(T)$, and we characterize all trees attaining equality. Also we prove that for every tree $T$ of order $n\ge 2$, $i(T)\le \frac{3\beta_{2}(T)}{4}$, and we characterize all extreme trees.

Keywords:

2-independence number, domination number, independent domination number