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

Document Type: Communication

Author

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

Abstract

\emph{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 $k=5,6$.

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