The rainbow connection number of enhanced power graph

Let $G$ be a finite group, the enhanced power graph of $G$, denoted by $Gamma_G^e$, is the graph with vertex set $G$ and two vertices $x,y$ are edge connected in $Gamma_{G}^e$ if there exist $zin G$ such that $x,yinlangle zrangle$. Let $zeta$ be a edge-coloring of $Gamma_G^e$. In this article, we calculate the rainbow connection number of the enhanced power graph $Gamma_G^e$.