Remarks on Bounds of Normalized Laplacian Eigenvalues of Graphs

Abstract

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 ${\rho }_i$, $i=1,2,\dots ,n-1$, are determined in terms of $n$ and general Randi\' c index, $R_{-1}$.