a note on the power graph of a finite group

‎ suppose γ is a graph with v(γ)={1‎,‎2,…‎,‎p} ‎and f={γ1,…‎,‎γp}is a family of‎ ‎graphs such that nj=|v(γj)‎, ‎1≤j≤p‎. ‎define‎ ‎λ=γ[γ1,…‎,‎γp] to be a graph with‎ ‎vertex set v(λ)=⋃pj=1v(γj) and edge set‎ ‎e(λ)=(⋃pj=1e(γj))∪(⋃ij∈‎‎e(γ){uv;u∈v(γi),v∈v(γj)}). ‎the‎ ‎graph λ is called the γ-join of ff‎. ‎the power graph p(g) of a group g is the graph‎ ‎which has the group elements as vertex set and two elements are‎ ‎adjacent if one is a power of the other‎. ‎the aim of this paper is‎ ‎to prove that p(zn)=kϕ(n)+1‎+‎δn[kϕ(d1)‎,‎kϕ(d2),…‎,‎kϕ(dp)]‎, ‎where δn is a graph with vertex and edge sets‎ v(δn)={di | 1,n≠di|n‎,‎1≤i≤p} and‎ ‎e(δn)={didj | di|dj‎,‎1≤i