20.500.12556/RUP-22065 The extremal generalised Randić index for a given degree range Ekstremni posplošeni Randićev indeks za dano območje stopenj O 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. Randić index bounded-degree graph extremal problem Randićev indeks graf z omejenimi stopnjami ekstremni problem true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 11:18:36 2025-11-03 11:18:36 2025-11-18 03:04:29 0000-00-00 00:00:00 2025 0 0 5 str. no. 2, [article no.] P2.02 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-03-12 51 2590-9770 10.26493/2590-9770.1759.1b8 ADAM_Haslegrave_2025.pdf ADAM_Haslegrave_2025.pdf 1 C11888C9A56418CE0C489328CFD03F03 c737d1e94f0818e2a2c8bcebfd6fe0793b1c5815c4e9e915169341abba153ef6 0968f3b7-b89f-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32010 Založba Univerze na Primorskem 0 0 0