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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 $Gamma_G^e$.
Let $k$ be a positive integer, and $G$ be a $k$-connected graph. An edge-coloured path is emph{rainbow} if all of its edges have distinct colours. The emph{rainbow $k$-connection number} of $G$, denoted by $rc_k(G)$, is the minimum number of colours
An edge-colored connected graph $G$ is properly connected if between every pair of distinct vertices, there exists a path that no two adjacent edges have a same color. Fujita (2019) introduced the optimal proper connection number ${mathrm{pc}_{mathrm
Let $F$ be a fixed graph. The rainbow Turan number of $F$ is defined as the maximum number of edges in a graph on $n$ vertices that has a proper edge-coloring with no rainbow copy of $F$ (where a rainbow copy of $F$ means a copy of $F$ all of whose e
An edge-cut $R$ of an edge-colored connected graph is called a rainbow-cut if no two edges in the edge-cut are colored the same. An edge-colored graph is rainbow disconnected if for any two distinct vertices $u$ and $v$ of the graph, there exists a $
An edge-coloured path is emph{rainbow} if all the edges have distinct colours. For a connected graph $G$, the emph{rainbow connection number} $rc(G)$ is the minimum number of colours in an edge-colouring of $G$ such that, any two vertices are connect