@article {
author = {Dehgardi, Nasrin and Sheikholeslami, Mahmoud and Khodkar, Abdollah},
title = {Bounding the rainbow domination number of a tree in terms of its annihilation number},
journal = {Transactions on Combinatorics},
volume = {2},
number = {3},
pages = {21-32},
year = {2013},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2013.3051},
abstract = {A $2$-rainbow dominating function (2RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2\}$ such that for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u\in N(v)}f(u)=\{1,2\}$ is fulfilled, where $N(v)$ is the open neighborhood of $v$. The weight of a 2RDF $f$ is the value $\omega(f)=\sum_{v\in V}|f (v)|$. The $2$-rainbow domination number of a graph $G$, denoted by $\gamma_{r2}(G)$, is the minimum weight of a 2RDF of G. The annihilation number $a(G)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $G$ is at most the number of edges in $G$. In this paper, we prove that for any tree $T$ with at least two vertices, $\gamma_{r2}(T)\le a(T)+1$.},
keywords = {annihilation number,2-rainbow dominating function,2-rainbow domination number},
url = {https://toc.ui.ac.ir/article_3051.html},
eprint = {https://toc.ui.ac.ir/article_3051_dc39b3b99937a3eea4c41cc51272e53a.pdf}
}