Let $\mathcal{P}(\mathbb Z_n)$ denote the power graph of $\mathbb Z_n$.
From this paper, "A note on the power graph of a finite group" https://ijgt.ui.ac.ir/article_6013_2f59939f01f22a9a5a68b464a1d66678.pdf I find that $\mathcal{P}(\mathbb Z_n)$ can be considered as the generalised join of graphs denoted by $G[K_{\phi(d_1)},K_{\phi(d_2)},\dots, K_{\phi(d_k)}]$ where $G$ has vertices $d_1<d_2<\dots<d_k$; $d_i$ is a positive proper divisor of $n$ and $d_i$ is adjacent to $d_j$ if and only if $d_i\mid d_j$ or vice versa.
In Theorem $2.3,$Page $5$ of the mentioned paper, the authors have determined the degree of each vertex of the graph as follows:
$\deg(x)=\phi(o(x))-2+\sum_{o(x)\mid d\mid n}\phi(d)$
However I am unable to figure out how they calculated it. Can someone please help me to understand how they got it?
If anyone can help, I will be grateful.
