Abstract
A coprime graph is a representation of finite groups on graphs by defining the vertex graph as an element in a group and two vertices adjacent to each other's if and only if the order of the two elements is coprime. In this research, we discuss the generalized Quaternion group and its properties. Then we discuss the properties of the coprime graph over the generalized Quaternion group by looking at its Eulerian, Hamiltonian, and Planarity sides. In general, the coprime graphs of the generalized quaternion group are not Eulerian, not Hamilton, and not planar graphs. The coprime graph of the generalized quaternion group is a planar graph if for a natural number .
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