The extremal generalised Randić index for a given degree rangeHaslegrave, John (Avtor) Randić indexbounded-degree graphextremal problemO and Shi proved that the Randić index of any graph G with minimum degree at least δ and maximum degree at most Δ is at least sqrt(δΔ)/(δ+Δ) |G|, with equality if and only if the graph is (δ, Δ)-biregular. In this note we give a short proof via a more general statement. As an application of our more general result, we classify for any given degree range which graphs minimise (or maximise) the generalised Randić index for any exponent, and describe the transitions between different types of behaviour precisely.Založba Univerze na Primorskem20252025-11-03 11:18:36Članek v reviji22065UDK: 51eISSN: 2590-9770DOI: 10.26493/2590-9770.1759.1b8sl