University of Isfahan Transactions on Combinatorics 2251-8657 2 1 2013 03 01 Bounding the domination number of a tree in terms of its annihilation number 9 16 2652 10.22108/toc.2013.2652 EN Nasrin Dehgardai Azarbaijan Shahid Madani University Sepideh Norouzian Azarbaijan Shahid Madani University Seyed Mahmoud Sheikholeslami Azarbaijan University of Tarbiat Moallem Journal Article 2012 07 26 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. https://toc.ui.ac.ir/article_2652_424dc767de5dc6d68475c6d0b1d46b2e.pdf