The rainbow connection number of enhanced power graph

Abstract: 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 $z\in G$ such that $x,y\in\langle z\rangle$. Let $\zeta$ be a edge-coloring of $\Gamma_G^e$. In this article, we calculate the rainbow connection number of the enhanced power graph $\Gamma_G^e$.