@article {
author = {Dehgardai, Nasrin and Norouzian, Sepideh and Sheikholeslami, Seyed Mahmoud},
title = {Bounding the domination number of a tree in terms of its annihilation number},
journal = {Transactions on Combinatorics},
volume = {2},
number = {1},
pages = {9-16},
year = {2013},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2013.2652},
abstract = {A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $V-S$ is adjacent to some vertex in $S$. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set in $G$. 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 show that for any tree $T$ of order $n\ge 2$, $\gamma(T)\le \frac{3a(T)+2}{4}$, and we characterize the trees achieving this bound.},
keywords = {annihilation number,dominating set,Domination Number},
url = {https://toc.ui.ac.ir/article_2652.html},
eprint = {https://toc.ui.ac.ir/article_2652_424dc767de5dc6d68475c6d0b1d46b2e.pdf}
}