University of IsfahanInternational Journal of Group Theory2251-765010320210901Parameters of the coprime graph of a group1371472469610.22108/ijgt.2020.112121.1489ENJessieHammDepartment of Mathematics, Winthrop University, 142 Bancroft Hall Rock Hill, SC, USAAlanWayDepartment of Mathematics, Winthrop University, 142 Bancroft Hall Rock Hill, SC, USAJournal Article20180726There 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