On the Regular Power Graph on the Conjugacy Classes of Finite Groups - Sajjad Mahmood Robati (Mathematics Interdisciplinary Research, 2018)
The (undirected) power graph on the conjugacy classes PC(G) of a group G  is a simple graph in which the vertices are the conjugacy classes of G and two distinct vertices C and C' are adjacent in PC(G) if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are k-regular for k=5,6.