%A Khoeilar, R. %A Aram, H. %A Sheikholeslami, S. M. %A Volkmann, L. %D 2018 %T Relating the annihilation number and the Roman domination %K %X A {\em Roman dominating function} (RDF) on a graph $G$ is a labeling $f\:$V (G)\rightarrow \{0, 1, 2\}$ such that every vertex with label 0 has a neighbor with label 2. The {\em weight} of an RDF $f$ is the value $\omega(f)=\sum_{v\in V}f (v)$. The {\em Roman domination number} of a graph $G$, denoted by $\gamma_R(G)$, equals the minimum weight of an RDF on 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 $T$ of order at least two, $\gamma_{R}(T)\le \frac{4a(T)+2}{3}$. %U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/471 %J Acta Mathematica Universitatis Comenianae %0 Journal Article %P 1-13%V 87 %N 1 %@ 0862-9544 %8 2018-01-26