Metric and strong metric dimension in commuting graphs of finite groups

The commuting graph of a finite group is the undirected graph whose vertex set is the set of all elements of this group, and two distinct vertices are adjacent if they commute. In this paper, we characterize the strong metric dimension of the commuting graph of a finite group and give upper and lower bounds for the metric dimension of the commuting graph of a finite group. As applications, we compute the metric and strong metric dimension of the commuting graph of a dihedral group, a generalized quaternion group and a semidihedral group.