| Title: | The extremal generalised Randić index for a given degree range |
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| Authors: | ID Haslegrave, John (Author) |
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| Files: |  ADAM_Haslegrave_2025.pdf (403,78 KB)
MD5: C11888C9A56418CE0C489328CFD03F03
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | 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. |
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| Keywords: | Randić index, bounded-degree graph, extremal problem |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 12.03.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 5 str. |
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| Numbering: | Vol. 8, no. 2, [article no.] P2.02 |
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| PID: | 20.500.12556/RUP-22065  |
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| UDC: | 51 |
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| eISSN: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1759.1b8 |
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| Publication date in RUP: | 03.11.2025 |
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| Views: | 265 |
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| Downloads: | 1 |
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