| Title: | Symmetries of the Woolly Hat graphs |
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| Authors: | ID Berman, Leah (Author)
ID Koike Quintanar, Sergio Hiroki (Author)
ID Mochán, Elías (Author)
ID Ramos Rivera, Alejandra (Author)
ID Šparl, Primož (Author)
ID Wilson, Steve (Author) |
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| Files: |  PDF - Presentation file, download (555,34 KB)
MD5: 680BD2717ABDA58A0B26110444946330
 URL - Source URL, visit https://adam-journal.eu/index.php/ADAM/article/view/1617
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different "types" of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one "type" has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones. |
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| Keywords: | edge-transitive, vertex-transitive, tricirculant, Woolly Hat graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 24 str. |
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| Numbering: | Vol. 7, no. 2, [article no.] P2.06 |
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| PID: | 20.500.12556/DiRROS-20518  |
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| UDC: | 519.17 |
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| ISSN on article: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1617.83c |
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| COBISS.SI-ID: | 188232195 |
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| Note: |
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| Publication date in DiRROS: | 07.10.2024 |
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| Views: | 226 |
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| Downloads: | 93 |
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| Metadata: |    |
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