Cubic vertex-transitive graphs admitting automorphisms of large order

Potočnik, Primož (author), Toledo, Micael (author)

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 $6$.

• Language: English
• Keywords: cubic vertex-transitive graphs, multicirculants, automorphisms of large order
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 33 str.
• Numbering: Vol. 46, iss. 4, art. 133
• PID: 20.500.12556/RUL-148031
• UDC: 519.1
• ISSN on article: 0126-6705
• DOI: 10.1007/s40840-023-01526-x
• COBISS.SI-ID: 155100675
• Publication date in RUL: 26.07.2023

Record is a part of a journal

• Title: Bulletin of the Malaysian Mathematical Sciences Society
• Shortened title: Bull. Malays. Math. Sci. Soc.
• Publisher: Springer Nature, Malaysian Mathematical Sciences Society, Penerbit Universiti Sains Malaysia
• ISSN: 0126-6705
• COBISS.SI-ID: 515781657

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.