On a conjecture about the Randić index

A conjecture of Delorme, Favaron and Rautenbach [On the Randić index, Discrete Math. 257 (2002) 29–38] about the Randić index of a graph, in relation to its order and minimum degree, is refuted by the AutoGraphiX 2 system. Moreover, a modified conjecture is derived from presumably extremal graphs obtained with that system.