commuting conjugacy class graphs of finite groups

Suppose that g is a finite non-abelian group. define the graph γ(g) with the non-central conjugacy classes of g as vertex set and two distinct vertices a and b are adjacent if and only if there are x∈a and y∈b such that xy=yx. the graph γ(g) is called the commuting conjugacy class graph of g and introduced by mohammadian et al. in [a. mohammadian, a. erfanian, m. farrokhi d. g. and b. wilkens, triangle-free commuting conjugacy class graphs, j. group theory 19 (3) (2016) 1049-1061]. in this paper, the graph structure of the commuting conjugacy class graph of nilpotent groups of order n are obtained in which n is not divisible by p^5, for every prime factor p of n.