Line graph characterization of power graphs of finite nilpotent groups

Abstract

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.

19 pages, 6 figures

References in corpus (1)

• Forbidden subgraphs of power graphs

Cited by in corpus (1)

• On connectivity, domination number and spectral radius of the proper enhanced power graphs of finite nilpotent groups