| Title: | Distance-regular Cayley graphs over ℤpˢ ⊕ ℤp |
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| Authors: | ID Zhan, Xiongfeng (Author)
ID Lu, Lu (Author)
ID Huang, Xueyi (Author) |
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| Files: |  AMC_Zhan,Lu,Huang_2025.pdf (461,23 KB)
MD5: 2FA40F6D82655F6BA2B06E601D8ABDCA
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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: | In 2007, Miklavič and Potočnik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. Let p be an odd prime. In this paper, all distance-regular Cayley graphs over ℤps ⊕ ℤp are identified. It is shown that every such graph is isomorphic to a complete graph, a complete multipartite graph, or the line graph of a transversal design TD(r, p) with 2 ≤ r ≤ p − 1. |
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| Keywords: | distance-regular graph, Cayley graph, Schur ring, Fourier transformation, transversal design |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 14.02.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 18 str. |
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| Numbering: | Vol. 25, no. 1, [article no.] P1.06 |
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| PID: | 20.500.12556/RUP-21977  |
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| UDC: | 519.17 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3242.12b |
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| Publication date in RUP: | 21.10.2025 |
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| Views: | 329 |
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| Downloads: | 1 |
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