Connectivity Indices of Coprime Graphs over Generalized Quaternion Groups of a Certain Order

The generalized quaternion group is a non-abelian group of order that exhibits certain structural similarities with the dihedral group. It is generated by two elements that satisfy specific defining relations. Meanwhile, a coprime graph is constructed by representing the elements of a group as vertices, where two vertices are adjacent if the orders of the corresponding elements are coprime. In this study, we investigate coprime graphs derived from generalized quaternion groups, particularly when the group order is given by , with being a prime number. Based on the structural properties of these graphs, we compute several connectivity indices, including the First and Second Zagreb indices, the Wiener index, the hyper-Wiener index, the Harary index, and the Szeged index.