Parameters of the coprime graph of a group

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 ΓG, 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. Keywords