A note on the power graph of a finite group

‎Suppose \Gamma is a graph with V(\Gamma) = \{ ۱‎, ‎۲,\dots‎, ‎p\}‎ ‎and \mathcal{F} = \{\Gamma_۱,\dots‎, ‎\Gamma_p\} is a family of‎ ‎graphs such that n_j = |V(\Gamma_j)|‎, ‎۱ \leq j \leq p‎. ‎Define‎ ‎\Lambda = \Gamma[\Gamma_۱,\dots‎, ‎\Gamma_p] to be a graph with‎ ‎vertex set V(\Lambda)=\bigcup_{j=۱}^pV(\Gamma_j) and edge set‎ ‎E(\Lambda)=\big(\bigcup_{j=۱}^pE(\Gamma_j)\big)\cup\big(\bigcup_{ij\in‎ ‎E(\Gamma)}\{uv;u\in V(\Gamma_i),v\in V(\Gamma_j)\}\big) ‎. ‎The‎ ‎graph \Lambda is called the \Gamma-join of \mathcal{F}‎. ‎The power graph \mathcal{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 \mathcal{P}(\mathbb{Z}_{n}) = K_{\phi(n)+۱}‎ + ‎\Delta_n[K_{\phi(d_۱)}‎, ‎K_{\phi(d_۲)},\dots‎, ‎K_{\phi(d_{p})}]‎, ‎where \Delta_n is a graph with vertex and edge sets‎ ‎V(\Delta_n)=\{d_i \ | \ ۱,n\not = d_i | n‎, ‎۱\leq i\leq p\} and‎ ‎ E(\Delta_n)=\{ d_id_j \ | \ d_i|d_j‎, ‎۱\leq i