Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree

Montero, Antonio (author), Potočnik, Primož (author)

The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper, we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results, we classify vertex-transitive graphs whose motion is 4 or a prime number.

• Language: English
• Keywords: fixity, motion, minimal degree, graphs, permutation groups
• 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: 2025
• Number of pages: 30 str.
• Numbering: Vol. 216, art. 106065
• PID: 20.500.12556/RUL-169451
• UDC: 519.17:512
• ISSN on article: 0097-3165
• DOI: 10.1016/j.jcta.2025.106065
• COBISS.SI-ID: 237036803
• Publication date in RUL: 29.05.2025

Record is a part of a journal

• Title: Journal of combinatorial theory
• Shortened title: J. comb. theory. Ser. A
• Publisher: Academic Press
• ISSN: 0097-3165
• COBISS.SI-ID: 25721344

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0294
• Name: Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: N1-0216
• Name: Simetrije, negibnost in prožnost grafov