A note on the coprime graph of a group

‎In this paper we study the coprime graph of a group $G$‎. ‎The‎ ‎coprime graph of a group $G$‎, ‎denoted by $Gamma_G$‎, ‎is a graph‎ ‎whose vertices are elements of $G$ and two distinct vertices $x$‎ ‎and $y$ are adjacent if and only if $(|x|,|y|)=1$‎. ‎In this paper‎, ‎we ‎show that $chi(Gamma_G)=omega(Gamma_G).$ We classify all the‎ ‎groups which $Gamma_G$ is a complete $r$partite graph or a‎ ‎planar graph‎. ‎Also we study the automorphism group of‎ ‎$Gamma_G$‎.