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Let $k$ be a positive integer. A $k$-rainbow domination function (kRDF) of agraph $G$ is a function $f$ from $V(G)$ to the set of all subsets of$\{1,2,\dots,k\}$ such that every vertex $v \in V(G)$ with $f(v) = \emptyset$satisfies $\bigcup_{u \in N(v)} f(u) = \{1,2,\dots,k\}$. The weight of a $k$RDFis defined as $w(f)= \sum_{v \in V(G)} |f(v)|$. The $k$-rainbow dominationnumber of $G$, denoted by $\gamma_{rk}(G)$, is the minimum weight of all kRDFsof $G$. In this paper, we determine the exact value of the 2-rainbow dominationnumber of circulant graphs $C(n; \{1,4\})$, which is $\gamma_{r2}(C(n;\{1,4\})) = \lceil n/3 \rceil + \alpha$, where $\alpha = 0$ for $n \equiv 0\pmod{6}$, $\alpha = 1$ for $n \equiv 1,2,3,5 \pmod{6}$, and $\alpha = 2$ for$n \equiv 4 \pmod{6}$.

2-Rainbow domination number of circulant graphs C(n; {1,4})