Title: | Cubic vertex-transitive graphs admitting automorphisms of large order |
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Authors: | ID Potočnik, Primož (Author) ID Toledo, Micael (Author) |
Files: | URL - Source URL, visit https://link.springer.com/article/10.1007/s40840-023-01526-x
PDF - Presentation file, download (929,04 KB) MD5: 790A1A6A18EA128B3BBC5528B27A6A67
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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 connected graph of order $n$ admitting a semiregular automorphism of order $n/k$ is called a $k$-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper, we study the broader class of cubic vertex-transitive graphs of order $n$ admitting an automorphism of order $n/3$ or larger that may not be semiregular. In particular, we show that any such graph is either a $k$-multicirculant for some $k \le 3$, or it belongs to an infinite family of graphs of girth $6$. |
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Keywords: | cubic vertex-transitive graphs, multicirculants, automorphisms of large order |
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Publication status: | Published |
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Publication version: | Version of Record |
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Publication date: | 01.07.2023 |
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Year of publishing: | 2023 |
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Number of pages: | art. 133 (33 str.) |
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Numbering: | Vol. 46, iss. 4 |
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PID: | 20.500.12556/DiRROS-18433 |
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UDC: | 519.1 |
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ISSN on article: | 0126-6705 |
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DOI: | 10.1007/s40840-023-01526-x |
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COBISS.SI-ID: | 155100675 |
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Note: |
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Publication date in DiRROS: | 18.03.2024 |
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Views: | 494 |
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Downloads: | 222 |
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