  Let $G$ be a connected undirected graph with $n$, $n\ge 3$, vertices and $m$
edges. Denote by $\rho_1 \ge \rho_2 \ge \cdots > \rho_n =0$ the normalized
Laplacian eigenvalues of $G$. Upper and lower bounds of $\rho_i$, $i=1,2,\ldots
, n-1$, are determined in terms of $n$ and general Randi\' c index, $R_{-1}$.

Spectral Theory