Metric and strong metric dimension in intersection power graphs of finite groups
Xuanlong Ma, Ruiqin Fu · Communications in Algebra · 2024
Let G be a finite group and let e be its identity element. The intersection power graph of G is the undirected graph with vertex set G, in which two distinct vertices x and y are adjacent if either 〈x〉∩〈y〉≠{e} or one of x and y is e. In this paper, we first compute the strong metric dimension of the intersection power graph of a cyclic group, a dihedral group, and a generalized quaternion group. We also characterize all finite groups G whose intersection power graph has strong metric dimension |G|−2. Then, we give the sharp upper and lower bounds for the metric dimension of the intersection power graph of a finite group. As applications, we obtain the metric dimension of the intersection power graph of a cyclic group, a dihedral group, a generalized quaternion group, and a group of odd order.