The undirected power graph on the conjugacy classes of a finite group

Let G be a finite group. The undirected power graph on the conjugacy classes of G is the simple graph PC(G) whose vertices are the conjugacy classes of G and two distinct vertices C and $C'$ are adjacent if one is a subset of a power of the other. In this paper, we show that the graph PC(G) is $2$-connected whenever either |π(G)|>1 or Z(G) is cyclic. Moreover, we classify finite groups G whose associated graph PC(G)-\ are bipartite.