University of Isfahan International Journal of Group Theory 2251-7650 10 3 2021 09 01 Parameters of the coprime graph of a group 137 147 24696 10.22108/ijgt.2020.112121.1489 EN Jessie Hamm Department of Mathematics, Winthrop University, 142 Bancroft Hall Rock Hill, SC, USA Alan Way Department of Mathematics, Winthrop University, 142 Bancroft Hall Rock Hill, SC, USA Journal Article 2018 07 26 ‎There are many different graphs one can associate to a group‎. ‎Some examples are the well-known Cayley graph‎, ‎the zero divisor graph (of a ring)‎, ‎the power graph‎, ‎and the recently introduced coprime graph of a group‎. ‎The coprime graph of a group $G$‎, ‎denoted $\Gamma_G$‎, ‎is the graph whose vertices are the group elements with $g$ adjacent to $h$ if and only if $(o(g),o(h))=1$‎. ‎In this paper we calculate the independence number of the coprime graph of the dihedral groups‎. ‎Additionally‎, ‎we characterize the groups whose coprime graph is perfect‎. https://ijgt.ui.ac.ir/article_24696_9bdd71ba7326bf96ac429abd41fd0412.pdf