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A path in an edge-colored graph $G$, where adjacent edges may have the samecolor, is called a rainbow path if no two edges of the path are colored thesame. The rainbow connection number $rc(G)$ of $G$ is the minimum integer $i$for which there exists an $i$-edge-coloring of $G$ such that every two distinctvertices of $G$ are connected by a rainbow path. The strong rainbow connectionnumber $src(G)$ of $G$ is the minimum integer $i$ for which there exists an$i$-edge-coloring of $G$ such that every two distinct vertices $u$ and $v$ of$G$ are connected by a rainbow path of length $d(u,v)$. In this paper, we giveupper and lower bounds of the (strong) rainbow connection Cayley graphs ofAbelian groups. Moreover, we determine the (strong) rainbow connection numbersof some special cases.

The (strong) rainbow connection numbers of Cayley graphs of Abelian groups