On the second smallest and the largest normalized Laplacian eigenvalues of a graph

Xiaoguo Tian, Ligong Wang, Yong Lu

Let $G$ be a simple connected graph with order $n$. Let $\mathcal{L}(G)$ be the normalized Laplacian matrix of $G$. Let ${\lambda }_k(G)$ be the $k$-th smallest normalized Laplacian eigen…