| Title: | A classification of Q-polynomial distance-regular graphs with girth 6 |
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| Authors: | ID Miklavič, Štefko (Author) |
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| Files: |  RAZ_Miklavic_Stefko_2025.pdf (291,61 KB)
MD5: E6FA55456B23AFD07C2BF177BC9F9699
 https://www.combinatorics.org/ojs/index.php/eljc/article/view/v32i4p60
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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: | IAM - Andrej Marušič Institute
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| Abstract: | Let Γ denote a Q-polynomial distance-regular graph with diameter D and valency k≥3. In [Homotopy in Q-polynomial distance-regular graphs, Discrete Math., {\bf 223} (2000), 189–206], H. Lewis showed that the girth of Γ is at most 6. In this paper we classify graphs that attain this upper bound. We show that Γ has girth 6 if and only if it is either isomorphic to the Odd graph on a set of cardinality 2D+1, or to a generalized hexagon of order (1,k−1). |
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| Keywords: | distance-regular graphs, Q-polynomial property, girth |
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| Publication version: | Version of Record |
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| Publication date: | 28.11.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-10 |
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| Numbering: | Vol. 32, iss. 4, article no. P4.60 |
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| PID: | 20.500.12556/RUP-22155  |
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| UDC: | 519.17 |
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| ISSN on article: | 1077-8926 |
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| DOI: | 10.37236/13897 |
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| COBISS.SI-ID: | 259293955 |
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| Publication date in RUP: | 01.12.2025 |
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| Views: | 177 |
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| Downloads: | 3 |
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| Metadata: |    |
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