The Coprime Graph of Groups
Alan Way · Digital Commons - Winthrop University (Winthrop University) · 2018
Recently, investigation of the coprime graph of a group was initiated. The coprime graph of a group is a graph with vertices as group elements and an edge between two vertices if and only if their order (in the group) is relatively prime. We will explore chromatic, clique, and independence number for certain classes of finite groups. In addition, we classify which abelian groups give rise to perfect coprime graphs. We obtain a partial result on the class of nonabelian groups.