Bounds and power means for the general Randic index

Clive Elphick, Pawel Wocjan

We review bounds for the general Randić 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…