On the Regular Power Graph on the Conjugacy Classes of Finite Groups

Document Type : Communication


Department of Mathematics, Faculty of science, Imam Khomeini international University


The (undirected) power graph on the conjugacy classes $\mathcal{P_C}(G)$ 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 $\mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.


Main Subjects

1. I‎. ‎Chakrabarty‎, ‎Sh‎. ‎Ghosh and M‎. ‎K‎. ‎Sen‎, ‎Undirected power graphs of semigroups‎, ‎Semigroup Forum 78 (2009) 410-426.
2. L‎. ‎Dornhoff‎, ‎Group Representation Theory‎. ‎Part A‎: ‎Ordinary Representation Theory‎, ‎Marcel Dekker‎, ‎New York‎, ‎1971‎.
3. G‎. ‎James and M‎. ‎Liebeck‎, Representations and Characters of Groups, ‎Cambridge University Press‎, Cambridge‎, ‎1993‎.
4. A‎. ‎V‎. ‎Lopez and J‎. ‎V‎. ‎Lopez‎, ‎Classification of finite groups according to the number of conjugacy classes‎, Israel J‎. ‎Math. 51 (1985) 305-338.
5. S‎. ‎M‎. ‎Robati‎, ‎The power graph on the conjugacy classes of a finite group‎, ‎Acta Math‎. ‎Hungar. 148(1) (2016) 109-116‎.