Bounds and power means for the general Randic index

We review bounds for the general Randi'c index, $R_{\alpha} = \sum_{ij \in E} (d_i d_j)^\alpha$, and use the power mean inequality to prove, for example, that $R_{\alpha }\ge m{\lambda }^{2\alpha }$ for $\alpha <0$, where $\lambda$ is the spectral radius of a graph. This enables us to strengthen various known lower and upper bounds for $R_{\alpha }$ and to generalise a non-spectral bound due to Bollob'as \emph{et al}. We also prove that the zeroth-order general Randi'c index, $Q_{\alpha }={\sum }_{i\in V}{d}_i^{\alpha }\ge n{\lambda }^{\alpha }$ for $\alpha < 0$.