The metric dimension of the enhanced power graph of a finite group

摘要

The enhanced power graph of a finite group G is the graph whose vertex set is G, and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this paper, we establish an explicit formula for the metric dimension of an enhanced power graph. As an application, we compute the metric dimension of the enhanced power graph of an elementary abelian p-group, a dihedral group and a generalized quaternion group.