Vertex-primitive digraphs with large fixity

Barbieri, Marco (author), Potočnik, Primož (author)

The relative fixity of a digraph $\Gamma$ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of $\Gamma$ and the number of vertices of $\Gamma$. We characterize the vertex-primitive digraphs whose relative fixity is at least $1 \over 3$, and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant.

• Language: English
• Keywords: vertex-primitive digraphs, fixity, product action, graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.10.2024
• Year: 2024
• Number of pages: Str. 2383-2403
• Numbering: Vol. 203, iss. 5
• PID: 20.500.12556/RUL-163177
• UDC: 519.17
• ISSN on article: 0373-3114
• DOI: 10.1007/s10231-024-01447-x
• COBISS.SI-ID: 195629059
• Publication date in RUL: 03.10.2024

Record is a part of a journal

• Title: Annali di matematica pura ed applicata
• Shortened title: Ann. mat. pura appl.
• Publisher: Springer
• ISSN: 0373-3114
• COBISS.SI-ID: 24962816

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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.