Forbidden subgraphs of conjugacy class graphs of groups

Let G be a finite group. The nilpotent/commuting/solvable conjugacy class graph is a simple graph with non-central conjugacy classes of G as its vertex set and two vertices are adjacent if and only if a member of one conjugacy class with a member of another conjugacy class generates a nilpotent/abelian/solvable (sub)group. In this paper have discussed about the forbidden subgraphs of nilpotent, commuting and solvable conjugacy class graphs of groups.