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 $k=5,6$.

A report on recent results and outstanding problems concerning motives associated to graphs.

Let G be a group, and $${{\,\mathrm{Sol}\,}}(G)=\{x \in : \langle x,y \rangle \text { is solvable for all } y G\}$$ . We associate graph $$\mathcal {NS}_G$$ (called the non-solvable of G) with whose vertex set $$G \setminus {{\,\mathrm{Sol}\,}}(G)$$ two distinct vertices are adjacent if they generate subgroup. In this paper, we study many properties particular, obtain results on degree, cardina...