The extremal generalised Randi\'c index for a given degree range
The extremal generalised Randi\'c index for a given degree range
O and Shi proved that the Randi\'c index of any graph $G$ with minimum degree at least $\delta$ and maximum degree at most $\Delta$ is at least $\frac{\sqrt{\delta\Delta}}{\delta+\Delta}|G|$, with equality if and only if the graph is $(\delta,\Delta)$-biregular. In this note we give a short proof via a more general …