  This paper deals with the classification of groups G such that power graphs
and proper power graphs of G are line graphs. In fact, We classify all finite
nilpotent groups whose power graphs are line graphs. Also we categorize all
finite nilpotent groups (except non abelian 2-groups) whose proper power graph
are line graphs. Moreover, we study that the proper power graphs of generalized
quaternion groups are line graphs. Besides, we derive a condition on the order
of the dihedral groups for which the proper power graphs of the dihedral groups
are line graphs.
