Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Line graph characterization of power graphs of finite nilpotent groups   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
graphs are line graphs. Moreover, we investigate when 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.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph