  For a simple connected graph $ G $ of order $ n $, the normalized Laplacian
is a square matrix of order $ n $, defined as $\mathcal{L}(G)=
D(G)^{-\frac{1}{2}}L(G)D(G)^{-\frac{1}{2}}$, where $ D(G)^{-\frac{1}{2}} $ is
the diagonal matrix whose $ i$-th diagonal entry is $ \frac{1}{\sqrt{d_{i}}} $.
In this article, we find the normalized Laplacian eigenvalues of the joined
union of regular graphs in terms of the adjacency eigenvalues and the
eigenvalues of quotient matrix associated with graph $ G $. For a finite group
$\mathcal{G}$, the power graph $\mathcal{P}(\mathcal{G})$ of a group $
\mathcal{G} $ is defined as the simple graph in which two distinct vertices are
joined by an edge if and only if one is the power of other. As a consequence of
the joined union of graphs, we investigate the normalized Laplacian eigenvalues
of power graphs of finite cyclic group $ \mathbb{Z}_{n}. $
